{
  "title": "Construction of tangents - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "🎯 Tangent touches circle at: ⭕", "options": {"A": "Two points", "B": "One point", "C": "Three points", "D": "No point"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "📐 From external point, number of tangents to circle: 🔢", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "🔺 Tangent is ______ to radius at point of contact: 📏", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Equal", "D": "Half"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "✏️ To construct tangent, we need: 🎨", "options": {"A": "Circle center & point", "B": "Only circle", "C": "Only point", "D": "Triangle"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "💫 Lengths of tangents from external point are: ⚖️", "options": {"A": "Equal", "B": "Different", "C": "Half", "D": "Double"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "🎨 First step in tangent construction: 1️⃣", "options": {"A": "Join point to center", "B": "Draw circle", "C": "Draw radius", "D": "Measure distance"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "🔍 Tangent makes ______ angle with radius: 📐", "options": {"A": "Acute", "B": "Obtuse", "C": "Right", "D": "Straight"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "⚡ From point on circle, number of tangents: 🌈", "options": {"A": "0", "B": "1", "C": "2", "D": "Infinite"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "📏 Tangent never ______ the circle: 🚫", "options": {"A": "Touches", "B": "Crosses", "C": "Meets", "D": "Intersects"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "🔵 Common tangent touches ______ circles: 🔴", "options": {"A": "One", "B": "Two", "C": "Three", "D": "Four"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "🟢 Direct common tangent crosses line joining centers: ✂️", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Always"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "🎯 Transverse common tangent crosses line joining centers: 🔄", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Always"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "📐 For tangent construction, we draw perpendicular at: 📍", "options": {"A": "Center", "B": "Midpoint", "C": "Point of contact", "D": "External point"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "💎 Two circles can have maximum ______ common tangents: 🔢", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "✏️ Tangent segment means part of tangent from: 🎯", "options": {"A": "Center to point", "B": "External point to circle", "C": "Circle to circle", "D": "Diameter end"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "🔺 Tangent from external point P, radius r, distance OP=d. Tangent length=? 📏", "options": {"A": "√(d² + r²)", "B": "√(d² - r²)", "C": "d + r", "D": "d - r"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "🎨 When point is inside circle, number of tangents: 🤔", "options": {"A": "0", "B": "1", "C": "2", "D": "Infinite"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "⚡ Two tangents from point P make angle θ at P. Angle between radii to contact points? 🔄", "options": {"A": "θ", "B": "180°-θ", "C": "90°-θ", "D": "2θ"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "📐 Concentric circles share: ⭐", "options": {"A": "Radius", "B": "Center", "C": "Tangent", "D": "Circumference"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "🔍 If point is on circle, tangent is ______ to radius at that point: 📏", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Equal", "D": "Half"}, "correct_answer": "B"},
    
    {"id": 21, "difficulty": "medium", "question": "🎯 Circle radius=5cm. Point P 13cm from center. Tangent length=? 📏", "options": {"A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "📐 Construct tangents from point 10cm from center of circle radius=6cm. How many tangents? 🔢", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "🔺 Two tangents from point P to circle of radius 7cm. If tangent length=24cm, OP=? ✏️", "options": {"A": "25 cm", "B": "26 cm", "C": "27 cm", "D": "28 cm"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "💫 Point P is 17cm from center O. Tangent length=15cm. Radius=? 🎯", "options": {"A": "6 cm", "B": "7 cm", "C": "8 cm", "D": "9 cm"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "🎨 Two tangents PA and PB from point P. If ∠APB=60°, ∠AOB=? (O=center) 🔄", "options": {"A": "60°", "B": "90°", "C": "120°", "D": "150°"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "⚡ Circle radius=8cm. External point 17cm away. Area of quadrilateral formed by tangents and radii? 📊", "options": {"A": "120 cm²", "B": "136 cm²", "C": "144 cm²", "D": "160 cm²"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "📏 Two circles radii 5cm & 3cm, centers 10cm apart. Number of direct common tangents? 🔍", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "🔵 Two circles radii 4cm & 2cm, centers 8cm apart. Number of transverse common tangents? ✂️", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "🟢 Tangent length=12cm, radius=5cm. Distance from point to center? 📐", "options": {"A": "13 cm", "B": "14 cm", "C": "15 cm", "D": "16 cm"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "🎯 Two tangents from point make 70° angle. Angle between radii to contact points? 🔄", "options": {"A": "70°", "B": "90°", "C": "110°", "D": "130°"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "✏️ Circle diameter=26cm. Point P 37cm from center. Tangent length=? 📏", "options": {"A": "35 cm", "B": "36 cm", "C": "37 cm", "D": "38 cm"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "💎 Concentric circles radii 7cm & 10cm. Can they have common tangent? 🤔", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Always"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "🔺 Point is 25cm from center. Tangent length=24cm. Area between tangents? 📊", "options": {"A": "168 cm²", "B": "192 cm²", "C": "216 cm²", "D": "240 cm²"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "📐 Two circles touch externally. Radii 6cm & 8cm. Length of direct common tangent? 🎨", "options": {"A": "8√3 cm", "B": "8√6 cm", "C": "4√15 cm", "D": "4√21 cm"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "⚡ From point on circle, tangent is drawn. Angle between tangent and chord through point equals: 🔍", "options": {"A": "Angle in opposite segment", "B": "Angle in same segment", "C": "Angle at center", "D": "Right angle"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "🎨 Two circles radii 9cm & 4cm, centers 15cm apart. Length of transverse common tangent? 📏", "options": {"A": "12 cm", "B": "√140 cm", "C": "√180 cm", "D": "√200 cm"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "💫 If distance between centers < |r1-r2|, number of common tangents? 🔢", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "🔵 Tangents from point to circle of radius 15cm are 20cm each. Distance from point to center? 📐", "options": {"A": "25 cm", "B": "30 cm", "C": "35 cm", "D": "40 cm"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "🟢 Two circles radii 5cm & 12cm, centers 25cm apart. Number of common tangents? ✂️", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "D"},
    {"id": 40, "difficulty": "medium", "question": "🎯 In right triangle circumscribed about circle, tangent points divide hypotenuse into segments of lengths? 📏", "options": {"A": "Radius each", "B": "Different", "C": "Equal to other sides", "D": "r and R"}, "correct_answer": "A"},
    
    {"id": 41, "difficulty": "hard", "question": "📐 Two circles radii 8cm & 3cm, centers 13cm apart. Length of direct common tangent? 🎨", "options": {"A": "12 cm", "B": "√120 cm", "C": "√132 cm", "D": "√156 cm"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "🔺 Three circles of radii 4cm, 5cm, 6cm touch externally pairwise. Area of triangle formed by their centers? 📊", "options": {"A": "√455 cm²", "B": "√525 cm²", "C": "√600 cm²", "D": "√675 cm²"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "💎 From point P, tangents PA and PB to circle. O is center. If PA=12cm, OA=5cm, area of quadrilateral OAPB? ✏️", "options": {"A": "60 cm²", "B": "65 cm²", "C": "70 cm²", "D": "75 cm²"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "⚡ Two circles radii 7cm & 1cm. Distance between centers=10cm. Length of transverse common tangent? 📏", "options": {"A": "6 cm", "B": "2√6 cm", "C": "4√2 cm", "D": "√80 cm"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "hard", "question": "🎨 Circle radius=√3 cm. From point P, tangents inclined at 60°. Distance OP? 🔍", "options": {"A": "2 cm", "B": "3 cm", "C": "2√3 cm", "D": "3√3 cm"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "📏 Two circles intersect orthogonally. Radii r1, r2. Distance between centers? 🤔", "options": {"A": "r1+r2", "B": "|r1-r2|", "C": "√(r1²+r2²)", "D": "√(r1²-r2²)"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "hard", "question": "🔵 Circle x²+y²=25. Tangent from point (7,0). Tangent length? 📐", "options": {"A": "2√6", "B": "√24", "C": "√26", "D": "√30"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "🟢 Two tangents from point (0,12) to circle x²+y²=25. Angle between tangents? 🔄", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "hard", "question": "🎯 Circle radius 5cm. External point P. Tangents PA, PB. If ∠APB=90°, OP=? 📏", "options": {"A": "5√2 cm", "B": "10 cm", "C": "5√3 cm", "D": "15 cm"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "✏️ Two circles radii 6cm & 14cm, centers 20cm apart. Direct common tangent length? 🎨", "options": {"A": "8√5 cm", "B": "8√6 cm", "C": "10√3 cm", "D": "12√2 cm"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "hard", "question": "💫 Three equal circles radius r touch each other. Area of triangle formed by centers? 📊", "options": {"A": "(√3/2)r²", "B": "(√3/4)r²", "C": "√3 r²", "D": "(√3/3)r²"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "hard", "question": "🔺 Two circles radii 4cm & 9cm, centers d cm apart. They have 3 common tangents. Range of d? 📐", "options": {"A": "5<d<13", "B": "d=13", "C": "d>13", "D": "d<5"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "hard", "question": "📐 Circle radius 8cm. Point P such that tangents from P make 60° angle. Distance OP? ⚡", "options": {"A": "8√3 cm", "B": "16 cm", "C": "16/√3 cm", "D": "8√3/3 cm"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "hard", "question": "🎨 From point P outside circle, tangents PA, PB. If OP=2OA, ∠APB=? 🔍", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "hard", "question": "⚡ Two circles radii 3cm & 5cm. Distance between centers=8cm. Number of transverse tangents? 🔢", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "hard", "question": "💎 Two circles touch internally. Radii 7cm & 1cm. Length of direct common tangent? 📏", "options": {"A": "√48 cm", "B": "√52 cm", "C": "√56 cm", "D": "√60 cm"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "🔵 Circle x²+y²=16. Tangents from point (6,0). Area between tangents? 📊", "options": {"A": "48√5", "B": "24√5", "C": "12√5", "D": "6√5"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "hard", "question": "🟢 Two circles radii R and r (R>r). Centers d apart. They have 4 common tangents if: ✂️", "options": {"A": "d>R+r", "B": "d=R+r", "C": "R-r<d<R+r", "D": "d<R-r"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "🎯 Tangents from point P to circle radius 10cm are 24cm each. Distance from P to nearest point on circle? 📐", "options": {"A": "14 cm", "B": "16 cm", "C": "18 cm", "D": "20 cm"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "📏 Two circles intersect. Maximum number of common tangents? 🔢", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"}
  ]
}