{
  "title": "Basic Terms Related to Circles - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "The set of all points in a plane equidistant from a fixed point is called a:", "options": {"A": "circle", "B": "radius", "C": "diameter", "D": "arc"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "The fixed point in a circle is called the:", "options": {"A": "center", "B": "radius", "C": "circumference", "D": "chord"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "A line segment joining any point on the circle to its center is called:", "options": {"A": "diameter", "B": "radius", "C": "chord", "D": "tangent"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "A chord passing through the center of a circle is called:", "options": {"A": "radius", "B": "diameter", "C": "arc", "D": "sector"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "A line that touches the circle at exactly one point is called:", "options": {"A": "chord", "B": "secant", "C": "tangent", "D": "radius"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "A line that intersects a circle at two distinct points is called:", "options": {"A": "tangent", "B": "secant", "C": "radius", "D": "diameter"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "A part of a circle between two points on it is called:", "options": {"A": "sector", "B": "segment", "C": "arc", "D": "chord"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "The region between a chord and its arc is called:", "options": {"A": "sector", "B": "segment", "C": "arc", "D": "radius"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "The region between two radii and an arc is called:", "options": {"A": "segment", "B": "sector", "C": "arc", "D": "chord"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "An arc less than a semicircle is called:", "options": {"A": "minor arc", "B": "major arc", "C": "semicircle", "D": "quadrant"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "An arc greater than a semicircle is called:", "options": {"A": "minor arc", "B": "major arc", "C": "semicircle", "D": "quadrant"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "Half of a circle is called:", "options": {"A": "minor arc", "B": "major arc", "C": "semicircle", "D": "quadrant"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "A quarter of a circle is called:", "options": {"A": "semicircle", "B": "quadrant", "C": "sextant", "D": "octant"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Equal chords are equidistant from the center. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "The perpendicular from the center to a chord bisects the chord. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "The longest chord of a circle is:", "options": {"A": "radius", "B": "diameter", "C": "tangent", "D": "secant"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "All radii of a circle are:", "options": {"A": "equal", "B": "unequal", "C": "parallel", "D": "perpendicular"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "The angle between a radius and a tangent at the point of contact is:", "options": {"A": "45°", "B": "60°", "C": "90°", "D": "180°"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "A quadrilateral whose vertices lie on a circle is called:", "options": {"A": "cyclic quadrilateral", "B": "regular quadrilateral", "C": "tangential quadrilateral", "D": "inscribed quadrilateral"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "The distance around a circle is called:", "options": {"A": "area", "B": "circumference", "C": "diameter", "D": "radius"}, "correct_answer": "B"},
    {"id": 21, "difficulty": "easy", "question": "If two chords are equal, their distances from the center are:", "options": {"A": "equal", "B": "unequal", "C": "inversely proportional", "D": "directly proportional"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "easy", "question": "The angle in a semicircle is:", "options": {"A": "acute", "B": "right", "C": "obtuse", "D": "straight"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "easy", "question": "Equal chords subtend equal angles at the center. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "easy", "question": "The perpendicular bisector of a chord passes through:", "options": {"A": "any point on circle", "B": "the center", "C": "midpoint of chord only", "D": "none of these"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "easy", "question": "A circle can have ______ parallel tangents at most.", "options": {"A": "one", "B": "two", "C": "three", "D": "infinite"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "easy", "question": "From an external point, ______ tangents can be drawn to a circle.", "options": {"A": "one", "B": "two", "C": "three", "D": "infinite"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "easy", "question": "Tangents drawn from an external point to a circle are:", "options": {"A": "equal", "B": "unequal", "C": "parallel", "D": "perpendicular"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "easy", "question": "The angle between two tangents drawn from an external point is supplementary to the angle between radii to points of contact. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "easy", "question": "The line joining the center to the midpoint of a chord is perpendicular to the chord. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "easy", "question": "A circle is symmetric about:", "options": {"A": "any diameter", "B": "center only", "C": "any chord", "D": "any tangent"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "easy", "question": "The distance from the center to any point on the circle is:", "options": {"A": "diameter", "B": "radius", "C": "chord", "D": "tangent"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "easy", "question": "If two circles intersect at two points, the line joining their centers is the perpendicular bisector of their common chord. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "easy", "question": "A chord is a diameter if and only if it is the longest chord. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "easy", "question": "There is exactly one tangent at a point on a circle. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "A"},
   {"id": 35, "difficulty": "easy", "question": "A circle has infinite lines of symmetry. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "A"}, {"id": 36, "difficulty": "easy", "question": "All chords of a circle are of different lengths. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "easy", "question": "The diameter divides the circle into two equal parts called:", "options": {"A": "quadrants", "B": "semicircles", "C": "segments", "D": "sectors"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "easy", "question": "Two circles are congruent if they have equal:", "options": {"A": "radii", "B": "diameters", "C": "both A and B", "D": "neither"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "easy", "question": "The point where tangent touches the circle is called:", "options": {"A": "center", "B": "point of contact", "C": "external point", "D": "midpoint"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "easy", "question": "A segment of a circle containing the center is called:", "options": {"A": "minor segment", "B": "major segment", "C": "semicircle", "D": "quadrant"}, "correct_answer": "B"},
    
    {"id": 41, "difficulty": "medium", "question": "In a circle of radius 5 cm, the length of a chord at distance 3 cm from center is:", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "Two chords AB and CD are at distances 4 cm and 3 cm from center respectively. If AB = 6 cm, find CD.", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "medium", "question": "In a circle, chord of length 24 cm is at distance 5 cm from center. Find radius.", "options": {"A": "7 cm", "B": "12 cm", "C": "13 cm", "D": "17 cm"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "From point P outside circle, two tangents PA and PB are drawn. If PA = 8 cm, find PB.", "options": {"A": "4 cm", "B": "8 cm", "C": "12 cm", "D": "16 cm"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "In circle of radius 10 cm, chord is 12 cm long. Find distance from center.", "options": {"A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "medium", "question": "Two concentric circles have radii 5 cm and 13 cm. Find length of chord of larger circle that touches smaller circle.", "options": {"A": "12 cm", "B": "18 cm", "C": "24 cm", "D": "26 cm"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "From external point P, tangents PA and PB are drawn to circle with center O. If ∠APB = 60°, find ∠AOB.", "options": {"A": "60°", "B": "90°", "C": "120°", "D": "150°"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "In circle, chord AB = 16 cm, distance from center = 6 cm. Find radius.", "options": {"A": "8 cm", "B": "10 cm", "C": "12 cm", "D": "14 cm"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "Two chords AB and CD are equidistant from center. If AB = 10 cm, find CD.", "options": {"A": "5 cm", "B": "10 cm", "C": "15 cm", "D": "20 cm"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "In circle, radius = 13 cm, distance of chord from center = 5 cm. Find length of chord.", "options": {"A": "12 cm", "B": "18 cm", "C": "24 cm", "D": "26 cm"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "medium", "question": "From point P, two tangents to circle of radius 7 cm are drawn. If length of tangent = 24 cm, find OP.", "options": {"A": "17 cm", "B": "25 cm", "C": "31 cm", "D": "49 cm"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "In circle, chord at distance 8 cm from center is 12 cm long. Find radius.", "options": {"A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "Two concentric circles have radii 8 cm and 15 cm. Chord of larger circle touches smaller circle. Find its length.", "options": {"A": "14 cm", "B": "21.6 cm", "C": "√161 cm", "D": "2√161 cm"}, "correct_answer": "D"},
    {"id": 54, "difficulty": "medium", "question": "From external point, tangents of length 15 cm are drawn to circle of radius 8 cm. Find distance from point to center.", "options": {"A": "17 cm", "B": "23 cm", "C": "25 cm", "D": "31 cm"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "In circle, chord length 30 cm is at distance 8 cm from center. Find radius.", "options": {"A": "15 cm", "B": "17 cm", "C": "19 cm", "D": "23 cm"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "Two chords are at distances 5 cm and 12 cm from center of radius 13 cm. Find the difference in their lengths.", "options": {"A": "2 cm", "B": "7 cm", "C": "14 cm", "D": "24 cm"}, "correct_answer": "C"},  {"id": 57, "difficulty": "medium", "question": "From point P outside circle, tangents PA and PB are drawn. If ∠APB = 50°, find ∠AOB where O is center.", "options": {"A": "50°", "B": "100°", "C": "130°", "D": "150°"}, "correct_answer": "C"}, {"id": 58, "difficulty": "medium", "question": "In circle of radius 25 cm, chord is 14 cm from center. Find its length.", "options": {"A": "24 cm", "B": "36 cm", "C": "48 cm", "D": "50 cm"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "medium", "question": "Two concentric circles have radii 9 cm and 15 cm. Chord of larger circle that touches smaller circle has length:", "options": {"A": "12 cm", "B": "18 cm", "C": "24 cm", "D": "30 cm"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "From point 17 cm from center, tangents of length 15 cm are drawn. Find radius.", "options": {"A": "5 cm", "B": "7 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 61, "difficulty": "medium", "question": "In circle, chord length 40 cm is 9 cm from center. Find radius.", "options": {"A": "20 cm", "B": "21 cm", "C": "24 cm", "D": "29 cm"}, "correct_answer": "D"},
    {"id": 62, "difficulty": "medium", "question": "A chord at distance 7 cm from center of radius 25 cm has length:", "options": {"A": "24 cm", "B": "40 cm", "C": "48 cm", "D": "50 cm"}, "correct_answer": "C"}, {"id": 63, "difficulty": "medium", "question": "From point P, tangents to circle of radius 6 cm are drawn. If length of tangent = 8 cm, find OP.", "options": {"A": "8 cm", "B": "10 cm", "C": "12 cm", "D": "14 cm"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "In circle, chord at distance 15 cm from center has length 40 cm. Find radius.", "options": {"A": "20 cm", "B": "25 cm", "C": "30 cm", "D": "35 cm"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "Two concentric circles have radii 12 cm and 20 cm. Chord of larger circle touching smaller circle has length:", "options": {"A": "16 cm", "B": "24 cm", "C": "32 cm", "D": "40 cm"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "From point 26 cm from center, tangents of length 24 cm are drawn. Find radius.", "options": {"A": "8 cm", "B": "10 cm", "C": "12 cm", "D": "14 cm"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "In circle, chord length 48 cm is 10 cm from center. Find radius.", "options": {"A": "24 cm", "B": "26 cm", "C": "28 cm", "D": "30 cm"}, "correct_answer": "B"},
  {"id": 68, "difficulty": "medium", "question": "A chord at distance 9 cm from center of radius 41 cm has length:", "options": {"A": "40 cm", "B": "58 cm", "C": "80 cm", "D": "82 cm"}, "correct_answer": "C"},  {"id": 69, "difficulty": "medium", "question": "From point P, tangents to circle of radius 8 cm are drawn. If length of tangent = 15 cm, find OP.", "options": {"A": "15 cm", "B": "17 cm", "C": "20 cm", "D": "23 cm"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "In circle, chord at distance 12 cm from center has length 70 cm. Find radius.", "options": {"A": "25 cm", "B": "30.5 cm", "C": "35 cm", "D": "37 cm"}, "correct_answer": "D"},
    {"id": 71, "difficulty": "medium", "question": "Two concentric circles have radii 7 cm and 25 cm. Chord of larger circle touching smaller circle has length:", "options": {"A": "14 cm", "B": "24 cm", "C": "48 cm", "D": "50 cm"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "From point 10 cm from center, tangents of length 6 cm are drawn. Find radius.", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "9 cm"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "In circle, chord length 60 cm is 11 cm from center. Find radius.", "options": {"A": "25 cm", "B": "30 cm", "C": "31 cm", "D": "34 cm"}, "correct_answer": "C"},
   {"id": 74, "difficulty": "medium", "question": "A chord at distance 15 cm from center of radius 25 cm has length:", "options": {"A": "20 cm", "B": "30 cm", "C": "40 cm", "D": "50 cm"}, "correct_answer": "C"}, {"id": 75, "difficulty": "medium", "question": "From point P, tangents to circle of radius 9 cm are drawn. If length of tangent = 12 cm, find OP.", "options": {"A": "12 cm", "B": "15 cm", "C": "18 cm", "D": "21 cm"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "In circle, chord at distance 16 cm from center has length 60 cm. Find radius.", "options": {"A": "30 cm", "B": "32 cm", "C": "34 cm", "D": "36 cm"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "Two concentric circles have radii 16 cm and 34 cm. Chord of larger circle touching smaller circle has length:", "options": {"A": "30 cm", "B": "45 cm", "C": "60 cm", "D": "68 cm"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "From point 25 cm from center, tangents of length 20 cm are drawn. Find radius.", "options": {"A": "10 cm", "B": "12 cm", "C": "15 cm", "D": "18 cm"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "In circle, chord length 80 cm is 18 cm from center. Find radius.", "options": {"A": "34 cm", "B": "36 cm", "C": "40 cm", "D": "41 cm"}, "correct_answer": "D"},
   {"id": 80, "difficulty": "medium", "question": "A chord at distance 8 cm from center of radius 17 cm has length:", "options": {"A": "15 cm", "B": "30 cm", "C": "32 cm", "D": "34 cm"}, "correct_answer": "B"},
    {"id": 81, "difficulty": "hard", "question": "In a circle, two parallel chords of lengths 30 cm and 16 cm are on same side of center. Distance between them is 7 cm. Find radius.", "options": {"A": "15 cm", "B": "17 cm", "C": "19 cm", "D": "21 cm"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "Two parallel chords of lengths 24 cm and 10 cm are on opposite sides of center. Distance between them is 17 cm. Find radius.", "options": {"A": "11 cm", "B": "13 cm", "C": "15 cm", "D": "17 cm"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "Three parallel chords on same side of center have lengths 20 cm, 24 cm, 30 cm. Distances between consecutive chords are 1 cm. Find radius.", "options": {"A": "12.5 cm", "B": "13 cm", "C": "14 cm", "D": "15 cm"}, "correct_answer": "B"},
    {"id": 84, "difficulty": "hard", "question": "Two concentric circles have radii R and r (R>r). Chord of larger circle touches smaller circle. If chord length is 2√(R²-r²), prove this is maximum chord with this property.", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Cannot prove"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "In circle of radius 13 cm, two parallel chords of lengths 24 cm and 10 cm are on same side. Find distance between them.", "options": {"A": "7 cm", "B": "11 cm", "C": "15 cm", "D": "17 cm"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Two parallel chords of lengths 48 cm and 20 cm are on opposite sides of center. Distance between them is 34 cm. Find radius.", "options": {"A": "20 cm", "B": "24 cm", "C": "26 cm", "D": "30 cm"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "Three parallel chords on same side have lengths 14 cm, 16 cm, 18 cm. Distances between them are equal. If radius is 10 cm, find distance between chords.", "options": {"A": "1 cm", "B": "1.5 cm", "C": "2 cm", "D": "2.5 cm"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "From point P outside circle, two tangents PA and PB are drawn. Chord AB divides circle into two arcs of ratio 5:7. Find ∠APB.", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "75°"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "In circle, two chords AB and CD intersect at right angles at P. If AP = 4 cm, PB = 6 cm, CP = 3 cm, find PD.", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "Two circles intersect at A and B. Through A, line PAQ is drawn meeting circles at P and Q. Prove PB = QB.", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Cannot prove"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "In circle, chords AB and CD intersect at P. If AP = 5 cm, PB = 12 cm, CP = 6 cm, find PD.", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "D"},
    {"id": 92, "difficulty": "hard", "question": "Two parallel chords of lengths 36 cm and 48 cm are on same side of center. Distance between them is 3 cm. Find radius.", "options": {"A": "20 cm", "B": "24 cm", "C": "25 cm", "D": "30 cm"}, "correct_answer": "D"},
    {"id": 93, "difficulty": "hard", "question": "From point P, tangents PA and PB are drawn. Chord AC is drawn parallel to PB. Prove PC = PA.", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Cannot prove"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "In circle, chords AB and CD intersect at P. If AP = 8 cm, PB = 6 cm, and CP:PD = 2:3, find CP.", "options": {"A": "3.2 cm", "B": "4 cm", "C": "4.8 cm", "D": "5.6 cm"}, "correct_answer": "C"},
    {"id": 95, "difficulty": "hard", "question": "Two parallel chords of lengths 40 cm and 48 cm are on opposite sides. Distance between them is 44 cm. Find radius.", "options": {"A": "25 cm", "B": "26 cm", "C": "28 cm", "D": "30 cm"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "Three parallel chords have lengths 10 cm, 12 cm, 14 cm. Distance between first two is 1 cm, between last two is also 1 cm. Find radius.", "options": {"A": "√61 cm", "B": "√65 cm", "C": "√73 cm", "D": "√85 cm"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "From point P outside circle, tangents PA and PB are drawn. Through midpoint M of AB, line PM is extended to meet circle at Q. Prove PQ is diameter.", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Cannot prove"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "In circle, chords AB and CD intersect at P. If AP = 7 cm, PB = 5 cm, CP = 4 cm, find PD.", "options": {"A": "6 cm", "B": "7 cm", "C": "8 cm", "D": "8.75 cm"}, "correct_answer": "D"},
    {"id": 99, "difficulty": "hard", "question": "Two parallel chords of lengths 32 cm and 24 cm are on same side. Distance between them is 4 cm. Find radius.", "options": {"A": "18 cm", "B": "20 cm", "C": "22 cm", "D": "25 cm"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "Three parallel chords have lengths 16 cm, 20 cm, 24 cm. They are equally spaced. If radius is 15 cm, find distance between chords.", "options": {"A": "2 cm", "B": "3 cm", "C": "4 cm", "D": "5 cm"}, "correct_answer": "B"}
  ]
}