{
  "title": "Construction of Tangents to Circle - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "To draw tangent to circle at point on circle, we first draw:", "options": {"A": "Diameter", "B": "Radius", "C": "Chord", "D": "Secant"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "Tangent at point on circle is perpendicular to:", "options": {"A": "Chord", "B": "Diameter", "C": "Radius", "D": "Secant"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "From external point, number of tangents to circle:", "options": {"A": "1", "B": "2", "C": "3", "D": "0"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "To construct tangent from external point, we first join point to:", "options": {"A": "Point on circle", "B": "Center", "C": "Midpoint", "D": "Any point"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "Length of tangent from external point P to circle with center O and radius r, if OP = d, is:", "options": {"A": "√(d² + r²)", "B": "√(d² - r²)", "C": "√(r² - d²)", "D": "d² - r²"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Two tangents from external point are:", "options": {"A": "Equal", "B": "Unequal", "C": "Parallel", "D": "Perpendicular"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Angle between radius and tangent at point of contact:", "options": {"A": "45°", "B": "60°", "C": "90°", "D": "180°"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "To draw tangent without using center, we use:", "options": {"A": "Chord properties", "B": "Arc properties", "C": "Angle in semicircle", "D": "Parallel lines"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "Point of contact is intersection of:", "options": {"A": "Two chords", "B": "Two radii", "C": "Tangent and circle", "D": "Two tangents"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "If two circles touch externally, common tangents:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "Common tangents to two concentric circles:", "options": {"A": "0", "B": "1", "C": "2", "D": "4"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Direct common tangent touches circles on:", "options": {"A": "Same side", "B": "Opposite sides", "C": "Any side", "D": "Center"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Transverse common tangent touches circles on:", "options": {"A": "Same side", "B": "Opposite sides", "C": "Any side", "D": "Center"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Angle between two tangents from external point is θ, angle between radii to points of contact:", "options": {"A": "θ", "B": "180°-θ", "C": "90°-θ", "D": "2θ"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "If two circles touch internally, common tangents:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "In right triangle formed by radius, tangent and line joining external point to center, right angle is at:", "options": {"A": "Center", "B": "External point", "C": "Point of contact", "D": "Midpoint"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "To construct tangents to circle of radius 3 cm from point 5 cm from center, length of tangent:", "options": {"A": "3 cm", "B": "4 cm", "C": "5 cm", "D": "6 cm"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "Perpendicular to tangent at point of contact passes through:", "options": {"A": "Center", "B": "Midpoint of chord", "C": "Any point", "D": "External point"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Maximum number of tangents parallel to given line:", "options": {"A": "1", "B": "2", "C": "3", "D": "Infinite"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "Tangents at ends of diameter are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Equal", "D": "Intersecting"}, "correct_answer": "A"},

    {"id": 21, "difficulty": "medium", "question": "Construct circle radius 4 cm. From point 10 cm from center, construct tangents. Length of each tangent:", "options": {"A": "2√21 cm", "B": "2√29 cm", "C": "2√31 cm", "D": "2√41 cm"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Construct two concentric circles radii 5 cm and 3 cm. Construct tangent to smaller circle from point on larger circle. Length of tangent:", "options": {"A": "3 cm", "B": "4 cm", "C": "5 cm", "D": "6 cm"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "Construct circle radius 6 cm. From point P outside, tangents PA and PB make 60° angle. Find OP if O is center.", "options": {"A": "6√3 cm", "B": "12 cm", "C": "12√3 cm", "D": "18 cm"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "Construct two circles radii 7 cm and 3 cm with centers 15 cm apart. Construct direct common tangent. Its length:", "options": {"A": "√161 cm", "B": "√176 cm", "C": "√191 cm", "D": "√221 cm"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "Construct circle radius 5 cm. From point 13 cm from center, construct tangents. Angle between tangents:", "options": {"A": "2 sin⁻¹(5/13)", "B": "2 cos⁻¹(5/13)", "C": "2 tan⁻¹(5/12)", "D": "2 tan⁻¹(12/5)"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Construct two circles radii 8 cm and 2 cm touching externally. Construct common tangents. Number of common tangents:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "Construct circle diameter 10 cm. Construct tangents at ends of diameter. Angle between these tangents:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "D"},
    {"id": 28, "difficulty": "medium", "question": "Construct two circles radii 6 cm and 4 cm with centers 14 cm apart. Construct transverse common tangent. Its length:", "options": {"A": "√192 cm", "B": "√208 cm", "C": "√224 cm", "D": "√240 cm"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Construct circle radius 3 cm. Construct tangent making 30° with line through center. Distance from center to point where tangent meets this line:", "options": {"A": "3√3 cm", "B": "6 cm", "C": "3√2 cm", "D": "4.5 cm"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Construct two circles radii 5 cm and 3 cm intersecting with 4 cm common chord. Distance between centers:", "options": {"A": "2√5 cm", "B": "3√3 cm", "C": "4√2 cm", "D": "6 cm"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Construct circle radius 7 cm. From point P, tangents PA and PB. If PA = 24 cm, find OP.", "options": {"A": "25 cm", "B": "26 cm", "C": "27 cm", "D": "28 cm"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Construct two circles radii 9 cm and 4 cm with centers 20 cm apart. Number of common tangents:", "options": {"A": "2", "B": "3", "C": "4", "D": "0"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "Construct circle radius 8 cm. Construct tangent parallel to chord 12 cm long at distance 5 cm from center. Distance between tangent and chord:", "options": {"A": "3 cm", "B": "4 cm", "C": "5 cm", "D": "6 cm"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Construct two circles touch internally, radii 10 cm and 4 cm. Distance between centers:", "options": {"A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "14 cm"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Construct circle radius 6 cm. Construct two parallel tangents on opposite sides. Distance between them:", "options": {"A": "6 cm", "B": "9 cm", "C": "12 cm", "D": "15 cm"}, "correct_answer": "C"},
    {"id": 36, "difficulty": "medium", "question": "Construct two circles radii 12 cm and 5 cm with centers 17 cm apart. Construct direct common tangent. Length:", "options": {"A": "12 cm", "B": "13 cm", "C": "14 cm", "D": "15 cm"}, "correct_answer": "D"},
    {"id": 37, "difficulty": "medium", "question": "Construct circle radius 5 cm. Construct tangent from point on concentric circle radius 13 cm. Length of tangent:", "options": {"A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "Construct two circles radii 7 cm and 1 cm touching externally. Direct common tangent length:", "options": {"A": "4√3 cm", "B": "4√5 cm", "C": "4√6 cm", "D": "4√7 cm"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Construct circle radius 4 cm. From point P, tangents make 90° angle. Find OP.", "options": {"A": "4√2 cm", "B": "6 cm", "C": "8 cm", "D": "8√2 cm"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Construct two circles radii 11 cm and 3 cm with centers 20 cm apart. Transverse common tangent length:", "options": {"A": "√336 cm", "B": "√364 cm", "C": "√384 cm", "D": "√396 cm"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Construct circle radius 9 cm. Chord 12 cm long. Construct tangent parallel to chord. Distance from center to tangent:", "options": {"A": "3√5 cm", "B": "3√7 cm", "C": "3√10 cm", "D": "3√13 cm"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Construct two circles intersect with 8 cm common chord. Radii 5 cm and 4 cm. Distance between centers:", "options": {"A": "√7 cm", "B": "√13 cm", "C": "√21 cm", "D": "√29 cm"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "medium", "question": "Construct circle radius 10 cm. From point 26 cm from center, construct tangents. Area of quadrilateral formed by center, points of contact, and external point:", "options": {"A": "240 cm²", "B": "260 cm²", "C": "280 cm²", "D": "300 cm²"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Construct two circles radii 13 cm and 5 cm with direct common tangent 24 cm. Distance between centers:", "options": {"A": "26 cm", "B": "28 cm", "C": "30 cm", "D": "32 cm"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Construct circle radius 6 cm. Construct tangent making 45° with line joining center to point on circle. Length of tangent from that point to where it meets line:", "options": {"A": "6 cm", "B": "6√2 cm", "C": "12 cm", "D": "12√2 cm"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Construct two circles radii 8 cm and 2 cm with centers 10 cm apart. Number of common tangents:", "options": {"A": "2", "B": "3", "C": "4", "D": "0"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "Construct circle radius 7 cm. Chord 10 cm long. Construct tangents at ends of chord. Angle between tangents:", "options": {"A": "2 sin⁻¹(5/7)", "B": "2 cos⁻¹(5/7)", "C": "2 tan⁻¹(5/√24)", "D": "2 tan⁻¹(√24/5)"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "medium", "question": "Construct two circles touch internally. Larger radius 9 cm, distance between centers 5 cm. Smaller radius:", "options": {"A": "2 cm", "B": "3 cm", "C": "4 cm", "D": "5 cm"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "medium", "question": "Construct circle radius 5 cm. Construct two tangents inclined at 120°. Distance from intersection point to center:", "options": {"A": "5√3 cm", "B": "10 cm", "C": "10√3 cm", "D": "15 cm"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "Construct two circles radii 15 cm and 8 cm with transverse common tangent 17 cm. Distance between centers:", "options": {"A": "17 cm", "B": "19 cm", "C": "21 cm", "D": "23 cm"}, "correct_answer": "D"},
    {"id": 51, "difficulty": "medium", "question": "Construct circle radius 12 cm. From point on concentric circle radius 20 cm, construct tangent. Its length:", "options": {"A": "14 cm", "B": "15 cm", "C": "16 cm", "D": "17 cm"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "Construct two circles radii 6 cm and 4 cm with centers 16 cm apart. Direct common tangent length:", "options": {"A": "√220 cm", "B": "√228 cm", "C": "√236 cm", "D": "√244 cm"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "Construct circle radius 8 cm. Chord 15 cm long. Construct tangent parallel to chord. Distance between chord and tangent:", "options": {"A": "√17 cm", "B": "√23 cm", "C": "√31 cm", "D": "√39 cm"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "Construct two circles intersect with 12 cm common chord. Radii 10 cm and 8 cm. Distance between centers:", "options": {"A": "2√7 cm", "B": "2√13 cm", "C": "2√19 cm", "D": "2√21 cm"}, "correct_answer": "D"},
    {"id": 55, "difficulty": "medium", "question": "Construct circle radius 9 cm. From point 15 cm from center, construct tangents. Area between tangents and minor arc:", "options": {"A": "81(π/2 - sin⁻¹(3/5)) cm²", "B": "81(π - 2 sin⁻¹(3/5)) cm²", "C": "81(π - sin⁻¹(4/5)) cm²", "D": "81(2π - sin⁻¹(3/5)) cm²"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "Construct two circles radii 14 cm and 6 cm with centers 25 cm apart. Number of common tangents:", "options": {"A": "2", "B": "3", "C": "4", "D": "0"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "medium", "question": "Construct circle radius 10 cm. Construct tangent making 30° with diameter through point of contact. Length from point on diameter to tangent along perpendicular:", "options": {"A": "5√3 cm", "B": "10/√3 cm", "C": "10√3 cm", "D": "20/√3 cm"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Construct two circles radii 9 cm and 3 cm touching externally. Common external tangent length:", "options": {"A": "6√3 cm", "B": "6√5 cm", "C": "6√6 cm", "D": "6√7 cm"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Construct circle radius 7 cm. Construct two parallel tangents on same side. Distance between them if distance from center to line joining their points of contact is 5 cm:", "options": {"A": "2√6 cm", "B": "4√3 cm", "C": "4√6 cm", "D": "8√3 cm"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "Construct two circles radii 16 cm and 7 cm with centers 30 cm apart. Transverse common tangent length:", "options": {"A": "√595 cm", "B": "√651 cm", "C": "√715 cm", "D": "√787 cm"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "Construct circle radius 11 cm. Chord 16 cm long. Construct tangents at ends. Angle between tangents:", "options": {"A": "2 sin⁻¹(8/11)", "B": "2 cos⁻¹(8/11)", "C": "2 tan⁻¹(8/√57)", "D": "2 tan⁻¹(√57/8)"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "Construct two circles radii 10 cm and 4 cm with centers 18 cm apart. Direct common tangent length:", "options": {"A": "√280 cm", "B": "√288 cm", "C": "√296 cm", "D": "√304 cm"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "Construct circle radius 13 cm. From point on concentric circle radius 25 cm, construct tangent. Area of right triangle formed:", "options": {"A": "150 cm²", "B": "156 cm²", "C": "168 cm²", "D": "180 cm²"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "Construct two circles radii 12 cm and 5 cm intersecting orthogonally. Distance between centers:", "options": {"A": "13 cm", "B": "15 cm", "C": "17 cm", "D": "19 cm"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Construct circle radius 6 cm. Construct tangent making 60° with radius at point of contact. Distance along tangent from point of contact to where perpendicular from center meets it:", "options": {"A": "3√3 cm", "B": "6/√3 cm", "C": "6√3 cm", "D": "12/√3 cm"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Construct two circles radii 8 cm and 3 cm with centers 14 cm apart. Number of common tangents:", "options": {"A": "2", "B": "3", "C": "4", "D": "0"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "Construct circle radius 15 cm. Chord 24 cm long. Construct tangent parallel to chord. Distance from center to tangent:", "options": {"A": "6 cm", "B": "8 cm", "C": "9 cm", "D": "12 cm"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "Construct two circles radii 7 cm and 2 cm touching externally. Common internal tangent length:", "options": {"A": "2√10 cm", "B": "2√13 cm", "C": "2√15 cm", "D": "2√17 cm"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Construct circle radius 10 cm. Construct two tangents making 90° with each other. Area of quadrilateral formed by center and points:", "options": {"A": "100 cm²", "B": "150 cm²", "C": "200 cm²", "D": "250 cm²"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "Construct two circles radii 20 cm and 8 cm with centers 34 cm apart. Direct common tangent length:", "options": {"A": "30 cm", "B": "32 cm", "C": "34 cm", "D": "36 cm"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Construct circle radius 14 cm. From point 50 cm from center, construct tangents. Difference between area of triangle formed by points and area of sector:", "options": {"A": "196(√3 - π/3) cm²", "B": "196(2√3 - π/3) cm²", "C": "196(√3 - π/6) cm²", "D": "196(2√3 - π/6) cm²"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Construct two circles radii 9 cm and 4 cm with centers 15 cm apart. Transverse common tangent length:", "options": {"A": "√176 cm", "B": "√184 cm", "C": "√192 cm", "D": "√200 cm"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Construct circle radius 12 cm. Construct tangent making 45° with chord of length 12√2 cm through point of contact. Distance from center to chord:", "options": {"A": "6√2 cm", "B": "8√2 cm", "C": "10√2 cm", "D": "12√2 cm"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "Construct two circles radii 11 cm and 5 cm intersecting with 8√3 cm common chord. Distance between centers:", "options": {"A": "12 cm", "B": "13 cm", "C": "14 cm", "D": "15 cm"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "Construct circle radius 8 cm. Construct two parallel tangents. Area of rectangle formed by points of contact and intersection points of tangents with line through center perpendicular to them, if distance between tangents is 12 cm:", "options": {"A": "64 cm²", "B": "96 cm²", "C": "128 cm²", "D": "192 cm²"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "Construct two circles radii 13 cm and 6 cm with centers 24 cm apart. Number of common tangents:", "options": {"A": "2", "B": "3", "C": "4", "D": "0"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "Construct circle radius 10 cm. Construct tangent at end of chord that subtends 120° at center. Angle between tangent and chord:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "75°"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Construct two circles radii 7 cm and 3 cm touching internally. Distance between centers:", "options": {"A": "2 cm", "B": "3 cm", "C": "4 cm", "D": "5 cm"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "Construct circle radius 9 cm. Construct two tangents making 60° with each other. Perimeter of triangle formed by intersection point and points of contact:", "options": {"A": "18√3 cm", "B": "27 cm", "C": "27√3 cm", "D": "36 cm"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "Construct two circles radii 15 cm and 9 cm with centers 27 cm apart. Direct common tangent length:", "options": {"A": "18 cm", "B": "21 cm", "C": "24 cm", "D": "27 cm"}, "correct_answer": "D"},

    {"id": 81, "difficulty": "hard", "question": "Construct two circles with radii 8 cm and 3 cm whose centers are 13 cm apart. Construct all common tangents. Find area of quadrilateral formed by points of contact of direct common tangents and centers.", "options": {"A": "30√3 cm²", "B": "36√2 cm²", "C": "42 cm²", "D": "48 cm²"}, "correct_answer": "D"},
    {"id": 82, "difficulty": "hard", "question": "Construct circle radius 5 cm. Construct another circle touching this circle externally and also touching a line at distance 12 cm from center of first circle. Find radius of second circle if it lies between line and first circle.", "options": {"A": "3 cm", "B": "3.5 cm", "C": "4 cm", "D": "4.5 cm"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "Construct three circles with radii 4 cm, 5 cm, 6 cm touching each other externally. Construct common tangents to all pairs. Find area of triangle formed by intersection points of internal common tangents.", "options": {"A": "15√7 cm²", "B": "20√6 cm²", "C": "24√5 cm²", "D": "30√3 cm²"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Construct circle radius 7 cm. Construct square such that each side is tangent to circle and one vertex lies on circle. Find side of square.", "options": {"A": "7(√2+1) cm", "B": "7(√2-1) cm", "C": "14/(√2+1) cm", "D": "14/(√2-1) cm"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "Construct two circles radii 9 cm and 4 cm with centers 20 cm apart. Construct circle touching both circles externally and also touching their direct common tangent. Find its radius.", "options": {"A": "36/11 cm", "B": "42/11 cm", "C": "48/11 cm", "D": "54/11 cm"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Construct circle radius 10 cm. Construct regular hexagon circumscribed about circle. Construct circle inscribed in hexagon. Ratio of area of annulus between two circles to area of inner circle.", "options": {"A": "(4-π)/π", "B": "(π-3)/3", "C": "(4-π)/3", "D": "(π-2)/2"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "Construct two circles radii 12 cm and 5 cm intersecting at 60°. Distance between centers such that common chord subtends 60° at center of first circle and 90° at center of second circle.", "options": {"A": "13 cm", "B": "14 cm", "C": "15 cm", "D": "16 cm"}, "correct_answer": "B"},
    {"id": 88, "difficulty": "hard", "question": "Construct circle radius 6 cm. Construct equilateral triangle circumscribed about circle. Construct circle inscribed in triangle. Difference between areas of two circles.", "options": {"A": "12π cm²", "B": "18π cm²", "C": "24π cm²", "D": "27π cm²"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "Construct two circles radii 8 cm and 3 cm with centers 15 cm apart. Construct third circle touching both circles and their transverse common tangent. Find its radius if it lies on same side of tangent as smaller circle.", "options": {"A": "24/7 cm", "B": "30/7 cm", "C": "36/7 cm", "D": "48/7 cm"}, "correct_answer": "B"},
    {"id": 90, "difficulty": "hard", "question": "Construct circle radius 5 cm. From point 13 cm from center, construct tangents. Construct circle touching both tangents and also touching original circle externally. Find its radius.", "options": {"A": "15/8 cm", "B": "20/7 cm", "C": "25/6 cm", "D": "30/11 cm"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Construct three equal circles each touching other two and also touching two parallel lines 16 cm apart. Find radius of each circle.", "options": {"A": "4 cm", "B": "16/3 cm", "C": "6 cm", "D": "20/3 cm"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "Construct circle radius 7 cm. Construct square inscribed in circle. Construct circle inscribed in square. Construct square inscribed in this inner circle. Ratio of areas of two squares.", "options": {"A": "1:2", "B": "1:√2", "C": "1:4", "D": "√2:1"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Construct two circles radii 10 cm and 6 cm with centers 24 cm apart. Construct circle touching both circles and their direct common tangent on side opposite to smaller circle. Find its radius.", "options": {"A": "15/2 cm", "B": "20/3 cm", "C": "25/4 cm", "D": "30/7 cm"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "Construct circle radius 8 cm. Construct regular pentagon circumscribed about circle. Find ratio of area of pentagon to area of circle.", "options": {"A": "5 tan 54°/π", "B": "5 sin 36°/π", "C": "5 cot 36°/π", "D": "5 cos 36°/π"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Construct two circles radii 5 cm and 3 cm intersecting orthogonally. Construct circle touching both circles and passing through their points of intersection. Find its radius.", "options": {"A": "√34 cm", "B": "√41 cm", "C": "√45 cm", "D": "√53 cm"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Construct circle radius 6 cm. From point on circle, construct chord making 30° with tangent. Construct perpendicular from center to chord. Find area of triangle formed by center, point on circle, and foot of perpendicular.", "options": {"A": "9√3 cm²", "B": "12√3 cm²", "C": "15√3 cm²", "D": "18√3 cm²"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Construct two circles radii 9 cm and 4 cm with centers 18 cm apart. Construct two circles each touching both given circles externally and also touching each other. Find sum of their radii.", "options": {"A": "13 cm", "B": "14 cm", "C": "15 cm", "D": "16 cm"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "Construct circle radius 10 cm. Construct three equal circles inside it, each touching other two and also touching original circle. Find radius of each small circle.", "options": {"A": "10(2√3-3) cm", "B": "10(√3-1) cm", "C": "10(2-√3) cm", "D": "10(3-√3) cm"}, "correct_answer": "C"},
    {"id": 99, "difficulty": "hard", "question": "Construct two circles radii 7 cm and 2 cm with centers 12 cm apart. Construct circle touching both circles and their transverse common tangent on side of smaller circle. Find its radius.", "options": {"A": "42/13 cm", "B": "48/13 cm", "C": "56/13 cm", "D": "64/13 cm"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "Construct equilateral triangle side 12 cm. Construct circle inscribed in it. Construct three equal circles each touching two sides of triangle and inscribed circle. Find radius of each small circle.", "options": {"A": "√3 cm", "B": "2√3/3 cm", "C": "4√3/3 cm", "D": "2√3 cm"}, "correct_answer": "B"}
  ]
}