{
  "title": "Construction of Bisectors - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What instrument is used to draw a perpendicular bisector?", "options": {"A": "Protractor only", "B": "Ruler only", "C": "Compass and ruler", "D": "Divider only"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "How many equal parts does a perpendicular bisector divide a line segment into?", "options": {"A": "Two equal parts", "B": "Three equal parts", "C": "Four equal parts", "D": "Five equal parts"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "What is the angle between the original line and its perpendicular bisector?", "options": {"A": "45°", "B": "60°", "C": "90°", "D": "180°"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "To bisect a 60° angle, what angle would you get?", "options": {"A": "20°", "B": "30°", "C": "45°", "D": "15°"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "Which point lies on the perpendicular bisector of a line segment?", "options": {"A": "Endpoints of segment", "B": "Midpoint of segment", "C": "Any point on line", "D": "External point"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "How many arcs are drawn from each end when constructing perpendicular bisector?", "options": {"A": "One", "B": "Two", "C": "Three", "D": "Four"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "What does 'bisect' mean?", "options": {"A": "To copy", "B": "To extend", "C": "To divide into two equal parts", "D": "To measure"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "An angle bisector divides an angle into:", "options": {"A": "Two equal angles", "B": "Three equal angles", "C": "Four equal angles", "D": "Arbitrary angles"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Which tool is essential for angle bisector construction?", "options": {"A": "Set square", "B": "Compass", "C": "Divider", "D": "Scale only"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "The perpendicular bisector of a line is always:", "options": {"A": "Parallel to line", "B": "Perpendicular to line", "C": "Oblique to line", "D": "Coincident with line"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "If you bisect a 90° angle, each part measures:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "Which point is equidistant from endpoints of segment?", "options": {"A": "Any point on perpendicular bisector", "B": "Endpoints themselves", "C": "Midpoint only", "D": "External points"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "To construct angle bisector, arcs are drawn from:", "options": {"A": "Vertex only", "B": "Arms of angle", "C": "External point", "D": "Midpoint of arms"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Perpendicular bisector passes through:", "options": {"A": "One endpoint", "B": "Midpoint", "C": "External point", "D": "Vertex"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "Bisecting 120° angle gives two angles of:", "options": {"A": "40° each", "B": "50° each", "C": "60° each", "D": "70° each"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "Which construction doesn't require measuring with protractor?", "options": {"A": "Copying angle", "B": "Bisecting angle", "C": "Measuring angle", "D": "Drawing specific angle"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "The intersection point of perpendicular bisectors of triangle sides is:", "options": {"A": "Centroid", "B": "Incenter", "C": "Circumcenter", "D": "Orthocenter"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "Angle bisector of equilateral triangle's vertex angle creates:", "options": {"A": "Two 30° angles", "B": "Two 45° angles", "C": "Two 60° angles", "D": "Two 90° angles"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "When constructing perpendicular bisector, compass radius should be:", "options": {"A": "Less than half segment", "B": "Exactly half segment", "C": "More than half segment", "D": "Any radius"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Bisector of straight angle (180°) creates:", "options": {"A": "Two 60° angles", "B": "Two 90° angles", "C": "Two 45° angles", "D": "Two 120° angles"}, "correct_answer": "B"},
    
    {"id": 21, "difficulty": "medium", "question": "Construct perpendicular bisector of segment AB = 6 cm. What is distance from midpoint to A?", "options": {"A": "2 cm", "B": "3 cm", "C": "4 cm", "D": "6 cm"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "In constructing angle bisector of 75°, arcs from arms intersect. The line from vertex through intersection point creates angles of:", "options": {"A": "35° and 40°", "B": "37.5° each", "C": "30° and 45°", "D": "25° and 50°"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "If perpendicular bisector of 8 cm segment is drawn, what is distance from any point on bisector to each endpoint?", "options": {"A": "Always equal", "B": "Always different", "C": "Sometimes equal", "D": "Never equal"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "To bisect 48° angle using compass, what should be radius for arcs?", "options": {"A": "Fixed 2 cm", "B": "Any convenient radius", "C": "Exactly half arm length", "D": "Equal to arm length"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "In triangle ABC, angle bisector of ∠A meets BC at D. If ∠A = 80°, then ∠BAD = ?", "options": {"A": "20°", "B": "40°", "C": "60°", "D": "80°"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "When constructing perpendicular bisector, why must compass radius be > half segment?", "options": {"A": "To ensure arcs intersect", "B": "To make accurate measurement", "C": "To avoid overlapping", "D": "To save time"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Bisect 150° angle. Each resulting angle measures:", "options": {"A": "50°", "B": "65°", "C": "75°", "D": "85°"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "In right triangle, angle bisector of right angle creates two angles of:", "options": {"A": "30° each", "B": "40° each", "C": "45° each", "D": "60° each"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "Perpendicular bisector of chord of circle passes through:", "options": {"A": "Center of circle", "B": "Any point on circumference", "C": "Endpoint of chord", "D": "Midpoint only"}, "correct_answer": "A"},
   {"id": 30, "difficulty": "medium", "question": "If angle bisector divides angle into 2x + 10 and 3x - 20, find original angle.", "options": {"A": "60°", "B": "80°", "C": "100°", "D": "140°"}, "correct_answer": "D"},    {"id": 31, "difficulty": "medium", "question": "Construct bisector of 22.5° angle. What angles are created?", "options": {"A": "10° and 12.5°", "B": "11.25° each", "C": "15° and 7.5°", "D": "20° and 2.5°"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "Perpendicular bisectors of all sides of triangle are concurrent at point called:", "options": {"A": "Orthocenter", "B": "Centroid", "C": "Incenter", "D": "Circumcenter"}, "correct_answer": "D"},
    {"id": 33, "difficulty": "medium", "question": "Bisect 135° angle without protractor. Each part measures:", "options": {"A": "45°", "B": "60°", "C": "67.5°", "D": "75°"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "In constructing perpendicular bisector, if arcs don't intersect, what's wrong?", "options": {"A": "Radius too small", "B": "Radius too large", "C": "Wrong center", "D": "Incorrect angle"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Angle bisectors of triangle are concurrent at:", "options": {"A": "Circumcenter", "B": "Orthocenter", "C": "Incenter", "D": "Centroid"}, "correct_answer": "C"},
    {"id": 36, "difficulty": "medium", "question": "If perpendicular bisector of AB is line L, and P is on L, then:", "options": {"A": "PA = AB", "B": "PA = PB", "C": "PA = 2PB", "D": "PB = 2PA"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Construct angle bisector of 36° angle. Each resulting angle:", "options": {"A": "12°", "B": "15°", "C": "18°", "D": "20°"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "In rhombus, diagonals bisect each other at:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "D"},
    {"id": 39, "difficulty": "medium", "question": "To verify perpendicular bisector construction, measure distances from intersection to:", "options": {"A": "Endpoints", "B": "Midpoint only", "C": "Vertex", "D": "External point"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Bisector of 72° angle creates angles of:", "options": {"A": "30° and 42°", "B": "34° and 38°", "C": "36° each", "D": "40° and 32°"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "If angle bisector makes 25° with one arm, original angle was:", "options": {"A": "25°", "B": "50°", "C": "75°", "D": "100°"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "Perpendicular bisector of hypotenuse of right triangle passes through:", "options": {"A": "Right angle vertex", "B": "Midpoint of hypotenuse", "C": "Center of inscribed circle", "D": "Orthocenter"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "Construct 60° angle then bisect it. Final angle measures:", "options": {"A": "15°", "B": "20°", "C": "30°", "D": "45°"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "Angle bisector theorem states ratio of sides equals ratio of:", "options": {"A": "Other angles", "B": "Adjacent segments", "C": "Opposite sides", "D": "Altitudes"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "In isosceles triangle, angle bisector of vertex angle is also:", "options": {"A": "Median", "B": "Altitude", "C": "Perpendicular bisector", "D": "All of these"}, "correct_answer": "D"},
    {"id": 46, "difficulty": "medium", "question": "Bisect 108° angle. Each part:", "options": {"A": "48°", "B": "54°", "C": "60°", "D": "72°"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "To construct 45° angle without protractor, first construct:", "options": {"A": "30° angle", "B": "60° angle", "C": "90° angle", "D": "120° angle"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "Perpendicular bisector of side of equilateral triangle passes through:", "options": {"A": "Opposite vertex", "B": "Midpoint of other side", "C": "Incenter", "D": "Circumcenter"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "If angle is bisected twice, how many equal parts?", "options": {"A": "2", "B": "3", "C": "4", "D": "8"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "Bisector of 40° angle makes angles of:", "options": {"A": "10° and 30°", "B": "15° and 25°", "C": "18° and 22°", "D": "20° each"}, "correct_answer": "D"},
    {"id": 51, "difficulty": "medium", "question": "In parallelogram, angle bisectors of adjacent angles are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Coincident", "D": "Equal length"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "Construct perpendicular bisector of 5 cm segment. Distance from midpoint to ends:", "options": {"A": "2 cm", "B": "2.5 cm", "C": "3 cm", "D": "5 cm"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "Angle bisector of linear pair creates:", "options": {"A": "Two acute angles", "B": "Two right angles", "C": "One acute one obtuse", "D": "Two obtuse angles"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "Perpendicular bisector of segment joining (2,3) and (6,3) is:", "options": {"A": "x = 2", "B": "x = 4", "C": "y = 3", "D": "y = 4"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "Bisect 27° angle. Result:", "options": {"A": "12° and 15°", "B": "13.5° each", "C": "10° and 17°", "D": "14° and 13°"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "In triangle, if angle bisector is also altitude, triangle is:", "options": {"A": "Equilateral", "B": "Isosceles", "C": "Right", "D": "Scalene"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "To construct 22.5° angle, first construct then bisect:", "options": {"A": "45° angle", "B": "60° angle", "C": "90° angle", "D": "30° angle"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Perpendicular bisector of vertical line segment is:", "options": {"A": "Vertical", "B": "Horizontal", "C": "Diagonal", "D": "Curved"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "If angle bisector divides 3:2, smaller part is 36°, original angle:", "options": {"A": "60°", "B": "90°", "C": "120°", "D": "150°"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "Bisector of 300° reflex angle creates:", "options": {"A": "Two 120° angles", "B": "Two 150° angles", "C": "150° each", "D": "Two acute angles"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "In square, angle bisector of 90° creates:", "options": {"A": "Two 30° angles", "B": "Two 45° angles", "C": "Two 60° angles", "D": "Two 90° angles"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "Perpendicular bisector of diameter of circle passes through:", "options": {"A": "Center", "B": "Circumference", "C": "Endpoint", "D": "Chord midpoint"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Construct 15° angle by bisecting:", "options": {"A": "30° angle", "B": "45° angle", "C": "60° angle", "D": "90° angle"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "If perpendicular bisector of AB is same as angle bisector of ∠ACB, then triangle is:", "options": {"A": "Equilateral", "B": "Right isosceles", "C": "Scalene", "D": "Obtuse"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "Bisector of 0° angle is:", "options": {"A": "Not defined", "B": "Same ray", "C": "Perpendicular", "D": "Parallel"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "In rectangle, angle bisectors of opposite angles are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Coincident", "D": "Equal"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "Perpendicular bisector of segment from (0,0) to (0,8) is:", "options": {"A": "x = 0", "B": "y = 4", "C": "x = 4", "D": "y = 0"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "Bisect 18° angle. Result:", "options": {"A": "8° and 10°", "B": "9° each", "C": "7° and 11°", "D": "6° and 12°"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "Angle bisectors of supplementary angles are:", "options": {"A": "Parallel", "B": "Perpendicular only if angles equal", "C": "Always perpendicular", "D": "Coincident"}, "correct_answer": "B"},    {"id": 70, "difficulty": "medium", "question": "If perpendicular bisector passes through vertex, triangle is:", "options": {"A": "Right", "B": "Isosceles", "C": "Equilateral", "D": "Scalene"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "Construct 67.5° by bisecting:", "options": {"A": "90° angle", "B": "120° angle", "C": "135° angle", "D": "150° angle"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "Perpendicular bisector divides plane into:", "options": {"A": "2 regions", "B": "3 regions", "C": "4 regions", "D": "Infinite regions"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Bisector of 240° reflex angle creates:", "options": {"A": "Two 60° angles", "B": "Two 120° angles", "C": "120° each", "D": "Two acute angles"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "In regular pentagon, angle bisector creates angles of:", "options": {"A": "36°", "B": "54°", "C": "72°", "D": "108°"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "If perpendicular bisector of chord passes through center, chord is:", "options": {"A": "Radius", "B": "Diameter", "C": "Tangent", "D": "Arc"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "Bisector of 105° angle creates:", "options": {"A": "50° and 55°", "B": "52.5° each", "C": "60° and 45°", "D": "70° and 35°"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "Angle bisectors of vertical angles are:", "options": {"A": "Same line", "B": "Perpendicular", "C": "Parallel", "D": "Coincident"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Perpendicular bisector of horizontal segment is:", "options": {"A": "Horizontal", "B": "Vertical", "C": "Diagonal", "D": "Curved"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "Construct 7.5° by repeated bisecting of:", "options": {"A": "30° angle", "B": "45° angle", "C": "60° angle", "D": "90° angle"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "If angle bisector is also median, triangle is:", "options": {"A": "Equilateral", "B": "Isosceles", "C": "Right", "D": "Scalene"}, "correct_answer": "B"},
    
    {"id": 81, "difficulty": "hard", "question": "Construct perpendicular bisector of segment AB = 7.2 cm without measuring midpoint. Which step is crucial?", "options": {"A": "Draw arcs with radius > 3.6 cm", "B": "Draw arcs with radius = 7.2 cm", "C": "Use protractor for 90°", "D": "Measure exactly 3.6 cm first"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Angle bisector of ∠A in triangle ABC meets BC at D. If AB = 6 cm, AC = 8 cm, and BC = 10 cm, find BD:DC using angle bisector theorem.", "options": {"A": "2:3", "B": "3:4", "C": "4:5", "D": "5:6"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "Construct 75° angle using only compass and straightedge (no protractor). Which combination of constructions is needed?", "options": {"A": "60° + 15°", "B": "90° - 15°", "C": "45° + 30°", "D": "60° + 45°"}, "correct_answer": "C"},
    {"id": 84, "difficulty": "hard", "question": "Prove that perpendicular bisector of chord passes through center of circle. Which theorem is used?", "options": {"A": "Pythagoras theorem", "B": "Equal chords equidistant", "C": "Angle in semicircle", "D": "Congruent triangles"}, "correct_answer": "D"},
    {"id": 85, "difficulty": "hard", "question": "Construct triangle with sides 6 cm, 7 cm, 8 cm. Then construct angle bisector of largest angle. What special property does this bisector have?", "options": {"A": "It's shortest bisector", "B": "Divides opposite side proportionally", "C": "Is perpendicular to side", "D": "Equals altitude"}, "correct_answer": "B"},
    {"id": 86, "difficulty": "hard", "question": "In ΔABC, angle bisectors of ∠B and ∠C meet at I. If ∠A = 50°, find ∠BIC.", "options": {"A": "105°", "B": "115°", "C": "125°", "D": "135°"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "Construct regular hexagon using only compass and straightedge. How many angle bisectors needed to find center?", "options": {"A": "1", "B": "2", "C": "3", "D": "6"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "Given line segment AB and point P not on AB. Construct perpendicular from P to AB using only compass and straightedge. How many arcs minimum?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "Angle bisector of parallelogram's acute angle makes 25° with side. Find angles of parallelogram.", "options": {"A": "50°, 130°", "B": "60°, 120°", "C": "70°, 110°", "D": "80°, 100°"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Construct 22.5° angle without protractor. How many bisections needed from 90°?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 91, "difficulty": "hard", "question": "In ΔABC, perpendicular bisector of AB meets BC at D. If AC = 12 cm and BC = 18 cm, find DC if D lies between B and C.", "options": {"A": "6 cm", "B": "8 cm", "C": "9 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 92, "difficulty": "hard", "question": "Prove that three angle bisectors of triangle are concurrent. Which congruence criterion is primarily used?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Construct triangle with perimeter 15 cm and sides in ratio 2:3:4. Then construct all angle bisectors. Do they meet at one point?", "options": {"A": "Yes, always", "B": "No, never", "C": "Only in equilateral", "D": "Depends on triangle"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "In quadrilateral ABCD, angle bisectors of ∠A and ∠B meet at P, of ∠B and ∠C at Q, etc. What shape is PQRS?", "options": {"A": "Parallelogram", "B": "Rectangle", "C": "Cyclic quadrilateral", "D": "Trapezium"}, "correct_answer": "C"},
    {"id": 95, "difficulty": "hard", "question": "Construct perpendicular bisector of segment using only compass (no straightedge for drawing line). Is it possible?", "options": {"A": "Yes, with 6 arcs", "B": "No, straightedge essential", "C": "Yes, with 4 arcs", "D": "Only with ruler"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "Angle bisector of ∠A in ΔABC divides BC into BD = 4 cm and DC = 6 cm. If AB = 8 cm, find AC.", "options": {"A": "9 cm", "B": "10 cm", "C": "12 cm", "D": "14 cm"}, "correct_answer": "C"},
    {"id": 97, "difficulty": "hard", "question": "Construct incircle of triangle. Which point is center?", "options": {"A": "Intersection of medians", "B": "Intersection of altitudes", "C": "Intersection of angle bisectors", "D": "Intersection of perpendicular bisectors"}, "correct_answer": "C"},
    {"id": 98, "difficulty": "hard", "question": "Given angle of 54°, construct angle of 27° without measuring. How many bisections?", "options": {"A": "1", "B": "2", "C": "3", "D": "Cannot be done exactly"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Perpendicular bisectors of two sides of triangle intersect at circumcenter. What's distance from circumcenter to vertices?", "options": {"A": "Equal", "B": "Proportional to sides", "C": "In radius ratio", "D": "Different"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Construct angle of 105° using only compass and straightedge. Which construction sequence works?", "options": {"A": "90° + 15°", "B": "60° + 45°", "C": "180° - 75°", "D": "120° - 15°"}, "correct_answer": "B"}
  ]
}