{
  "title": "Circles: Chord, Diameter, Radius - Grade 5 ICSE",
  "total_questions": 100,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "The longest chord of a circle is called the ____. ⭕",
      "options": { "A": "Radius", "B": "Diameter", "C": "Arc", "D": "Sector" },
      "correct_answer": "B"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "The distance from the center to any point on the circle is the ____. 📏",
      "options": {
        "A": "Chord",
        "B": "Diameter",
        "C": "Radius",
        "D": "Circumference"
      },
      "correct_answer": "C"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "How many diameters can a circle have? 🔵",
      "options": { "A": "1", "B": "2", "C": "10", "D": "Infinite" },
      "correct_answer": "D"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "The diameter is ____ times the radius. ✖️",
      "options": { "A": "2", "B": "3", "C": "4", "D": "1/2" },
      "correct_answer": "A"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "A chord passing through the center becomes a ____. 🎯",
      "options": { "A": "Radius", "B": "Diameter", "C": "Arc", "D": "Tangent" },
      "correct_answer": "B"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "If radius = 7 cm, diameter = ____ cm. 📐",
      "options": { "A": "3.5", "B": "7", "C": "14", "D": "21" },
      "correct_answer": "C"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "All radii of a circle are ____. ⭕",
      "options": {
        "A": "Different",
        "B": "Equal",
        "C": "Parallel",
        "D": "Perpendicular"
      },
      "correct_answer": "B"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "A line segment joining two points on a circle is a ____. ↔️",
      "options": {
        "A": "Radius",
        "B": "Diameter",
        "C": "Chord",
        "D": "Tangent"
      },
      "correct_answer": "C"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "If diameter = 20 cm, radius = ____ cm. 📏",
      "options": { "A": "5", "B": "10", "C": "15", "D": "20" },
      "correct_answer": "B"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "The diameter divides the circle into two equal ____. 🔴",
      "options": {
        "A": "Chords",
        "B": "Arcs",
        "C": "Semicircles",
        "D": "Radii"
      },
      "correct_answer": "C"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "A circle has ____ center(s). ⭕",
      "options": { "A": "1", "B": "2", "C": "3", "D": "Many" },
      "correct_answer": "A"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "How many chords can be drawn in a circle? 🎯",
      "options": { "A": "1", "B": "2", "C": "10", "D": "Infinite" },
      "correct_answer": "D"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "The plural of radius is ____. 🔵",
      "options": {
        "A": "Radiuses",
        "B": "Radii",
        "C": "Radiusi",
        "D": "Radia"
      },
      "correct_answer": "B"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "A diameter is also a ____. ↔️",
      "options": { "A": "Radius", "B": "Chord", "C": "Arc", "D": "Tangent" },
      "correct_answer": "B"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "If radius = 5.5 cm, diameter = ____ cm. 📐",
      "options": { "A": "2.75", "B": "5.5", "C": "11", "D": "16.5" },
      "correct_answer": "C"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "The midpoint of a diameter is the ____. 🎯",
      "options": {
        "A": "Chord",
        "B": "Center",
        "C": "Arc",
        "D": "Circumference"
      },
      "correct_answer": "B"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "A circle is named by its ____. 🔤",
      "options": {
        "A": "Radius",
        "B": "Diameter",
        "C": "Center",
        "D": "Chord"
      },
      "correct_answer": "C"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "How many radii are equal to one diameter? ⚖️",
      "options": { "A": "1", "B": "2", "C": "3", "D": "4" },
      "correct_answer": "B"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "A chord that is not a diameter is ____ than the diameter. 📏",
      "options": { "A": "Longer", "B": "Shorter", "C": "Equal", "D": "Twice" },
      "correct_answer": "B"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "The diameter is the ____ chord. 🏆",
      "options": {
        "A": "Shortest",
        "B": "Longest",
        "C": "Thickest",
        "D": "Only"
      },
      "correct_answer": "B"
    },
    {
      "id": 21,
      "difficulty": "medium",
      "question": "If a chord is 24 cm long and is 5 cm from the center, what is the radius? (Use Pythagoras approx) 🔍",
      "options": { "A": "10 cm", "B": "12 cm", "C": "13 cm", "D": "15 cm" },
      "correct_answer": "C"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "The perpendicular from the center to a chord ____ the chord. ⚡",
      "options": {
        "A": "Bisects",
        "B": "Trisects",
        "C": "Equals",
        "D": "Extends"
      },
      "correct_answer": "A"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "Two chords equidistant from the center are ____. ↔️",
      "options": {
        "A": "Parallel",
        "B": "Equal",
        "C": "Perpendicular",
        "D": "Tangents"
      },
      "correct_answer": "B"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "If radius = 10 cm, the longest chord length is ____ cm. 📏",
      "options": { "A": "10", "B": "15", "C": "20", "D": "25" },
      "correct_answer": "C"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "A chord of length 16 cm is at distance 6 cm from center. Radius = ____ cm. 🔍",
      "options": { "A": "8", "B": "10", "C": "12", "D": "14" },
      "correct_answer": "B"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "How many diameters can be drawn through a given point on the circle? 🔵",
      "options": { "A": "1", "B": "2", "C": "3", "D": "Infinite" },
      "correct_answer": "A"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "In a circle, if a radius is perpendicular to a chord, it ____ the chord. ⚡",
      "options": {
        "A": "Equals",
        "B": "Bisects",
        "C": "Doubles",
        "D": "Parallels"
      },
      "correct_answer": "B"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "The diameter of a circle is 26 cm. A chord is 10 cm from center. Chord length = ____ cm. 📐",
      "options": {
        "A": "16.6",
        "B": "17",
        "C": "18",
        "D": "20"
      },
      "correct_answer": "A"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "Chords equal in length are ____ from the center. 📏",
      "options": {
        "A": "At different distances",
        "B": "Equidistant",
        "C": "Twice as far",
        "D": "Half as far"
      },
      "correct_answer": "B"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "If two chords intersect inside a circle, the products of their segments are ____. ✖️",
      "options": { "A": "Equal", "B": "Different", "C": "Half", "D": "Double" },
      "correct_answer": "A"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "A chord 12 cm long is 8 cm from center. Radius = ____ cm. 🔍",
      "options": { "A": "10", "B": "12", "C": "14", "D": "16" },
      "correct_answer": "A"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "The line joining the center to the midpoint of a chord is ____ to the chord. 📐",
      "options": {
        "A": "Parallel",
        "B": "Perpendicular",
        "C": "Equal",
        "D": "Tangential"
      },
      "correct_answer": "B"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "If a chord is 5 cm from center and radius is 13 cm, chord length = ____ cm. 📏",
      "options": { "A": "12", "B": "18", "C": "24", "D": "26" },
      "correct_answer": "C"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "How many chords of length equal to radius can be drawn in a circle? 🔵",
      "options": { "A": "1", "B": "2", "C": "6", "D": "Infinite" },
      "correct_answer": "D"
    },
    {
      "id": 35,
      "difficulty": "medium",
      "question": "The diameter is a special chord that passes through the ____. 🎯",
      "options": {
        "A": "Chord",
        "B": "Center",
        "C": "Arc",
        "D": "Circumference"
      },
      "correct_answer": "B"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "A chord subtends equal angles at the center if chords are ____. 📐",
      "options": {
        "A": "Parallel",
        "B": "Equal",
        "C": "Perpendicular",
        "D": "Different"
      },
      "correct_answer": "B"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "If a radius bisects a chord, it is ____ to the chord. ↔️",
      "options": {
        "A": "Parallel",
        "B": "Perpendicular",
        "C": "Equal",
        "D": "Half"
      },
      "correct_answer": "B"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "Radius = 15 cm, distance of chord from center = 9 cm. Chord length = ____ cm. 📏",
      "options": { "A": "12", "B": "18", "C": "24", "D": "30" },
      "correct_answer": "C"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "The longest distance between two points on a circle is the ____. 🏆",
      "options": { "A": "Radius", "B": "Chord", "C": "Diameter", "D": "Arc" },
      "correct_answer": "C"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "If two chords are equal, their distances from center are ____. ↔️",
      "options": { "A": "Different", "B": "Equal", "C": "Half", "D": "Double" },
      "correct_answer": "B"
    },
    {
      "id": 41,
      "difficulty": "hard",
      "question": "Two chords AB and CD intersect at E inside circle. If AE=4, EB=6, CE=3, find ED. 🔍",
      "options": { "A": "4", "B": "6", "C": "8", "D": "12" },
      "correct_answer": "C"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "In a circle of radius 10 cm, a chord is 6 cm from center. Find length of chord. 📐",
      "options": { "A": "12 cm", "B": "16 cm", "C": "18 cm", "D": "20 cm" },
      "correct_answer": "B"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "The radius of a circle is 13 cm. A chord is 5 cm from center. Find chord length. 🔍",
      "options": { "A": "12 cm", "B": "18 cm", "C": "24 cm", "D": "26 cm" },
      "correct_answer": "C"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "Two parallel chords are 8 cm and 6 cm long and are on same side of center. Distance between chords is 1 cm. Find radius. 🔵",
      "options": { "A": "5 cm", "B": "6 cm", "C": "7 cm", "D": "8 cm" },
      "correct_answer": "A"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "Chords AB and CD intersect at O inside circle. AO=3, OB=4, CO=6, find OD. 🔍",
      "options": { "A": "2", "B": "3", "C": "4", "D": "5" },
      "correct_answer": "A"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "In a circle, chord of length 24 cm is 5 cm from center. Find radius. 📏",
      "options": { "A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm" },
      "correct_answer": "D"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "Two chords equidistant from center are 12 cm and 16 cm long. Find distance of each from center if radius=10 cm. 🔍",
      "options": { "A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm" },
      "correct_answer": "A"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "A chord 8 cm long is 3 cm from center. Find radius. 🔵",
      "options": { "A": "4 cm", "B": "5 cm", "C": "6 cm", "D": "7 cm" },
      "correct_answer": "B"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "Two intersecting chords: AE=2, EB=8, CE=4, find ED. 🔍",
      "options": { "A": "4", "B": "6", "C": "8", "D": "16" },
      "correct_answer": "A"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "Radius=15 cm, distance of chord from center=12 cm. Find chord length. 📐",
      "options": { "A": "12 cm", "B": "18 cm", "C": "24 cm", "D": "30 cm" },
      "correct_answer": "B"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "In a 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": 52,
      "difficulty": "hard",
      "question": "Two parallel chords on opposite sides of center: lengths 16 cm and 12 cm, distance between chords=14 cm. Find radius. 🔵",
      "options": { "A": "8 cm", "B": "10 cm", "C": "12 cm", "D": "14 cm" },
      "correct_answer": "B"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "Chords PQ and RS intersect at T. PT=3, TQ=4, RT=6, find TS. 🔍",
      "options": { "A": "2", "B": "3", "C": "4", "D": "5" },
      "correct_answer": "A"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "A chord is 8 cm from center. Radius=17 cm. Find chord length. 📏",
      "options": {
        "A": "30 cm",
        "B": "32 cm",
        "C": "34 cm",
        "D": "36 cm"
      },
      "correct_answer": "A"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "Two chords intersect: AE×EB=CE×ED. If AE=5, EB=7, CE=10, find ED. ✖️",
      "options": { "A": "3.5", "B": "4", "C": "4.5", "D": "5" },
      "correct_answer": "A"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "Radius=25 cm, chord length=48 cm. Find distance from center to chord. 🔍",
      "options": { "A": "7 cm", "B": "10 cm", "C": "14 cm", "D": "20 cm" },
      "correct_answer": "A"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "Two chords AB=12 cm, CD=16 cm are equidistant from center. If radius=10 cm, find distance of each chord from center. 🔵",
      "options": { "A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm" },
      "correct_answer": "A"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "Chord length=30 cm, distance from center=8 cm. Find radius. 📐",
      "options": { "A": "15 cm", "B": "17 cm", "C": "20 cm", "D": "25 cm" },
      "correct_answer": "B"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "Two intersecting chords: AP=4, PB=9, CP=6, find PD. 🔍",
      "options": { "A": "4", "B": "6", "C": "8", "D": "10" },
      "correct_answer": "B"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "Radius=13 cm, chord length=10 cm. Find distance from center. 📏",
      "options": { "A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm" },
      "correct_answer": "C"
    },
    {
      "id": 61,
      "difficulty": "hard",
      "question": "In a circle, chord of length 14 cm is 24 cm from center. Find radius. 🔍",
      "options": {
        "A": "25 cm",
        "B": "26 cm",
        "C": "28 cm",
        "D": "30 cm"
      },
      "correct_answer": "A"
    },
    {
      "id": 62,
      "difficulty": "hard",
      "question": "Two chords intersect: segments are 3,4 and 2,x. Find x. 🔍",
      "options": { "A": "4", "B": "5", "C": "6", "D": "8" },
      "correct_answer": "C"
    },
    {
      "id": 63,
      "difficulty": "hard",
      "question": "Radius=20 cm, distance of chord=12 cm. Find chord length. 📐",
      "options": { "A": "16 cm", "B": "24 cm", "C": "32 cm", "D": "40 cm" },
      "correct_answer": "C"
    },
    {
      "id": 64,
      "difficulty": "hard",
      "question": "Two parallel chords 10 cm and 24 cm long are on same side of center, 7 cm apart. Find radius. 🔵",
      "options": { "A": "10 cm", "B": "12 cm", "C": "13 cm", "D": "15 cm" },
      "correct_answer": "C"
    },
    {
      "id": 65,
      "difficulty": "hard",
      "question": "Chords intersect: AE=2, EB=10, CE=4, find ED. 🔍",
      "options": { "A": "5", "B": "6", "C": "8", "D": "12" },
      "correct_answer": "A"
    },
    {
      "id": 66,
      "difficulty": "hard",
      "question": "Chord length=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": 67,
      "difficulty": "hard",
      "question": "Two chords AB=18 cm, CD=24 cm are equidistant from center. If radius=15 cm, find distance. 🔍",
      "options": { "A": "9 cm", "B": "10 cm", "C": "12 cm", "D": "15 cm" },
      "correct_answer": "A"
    },
    {
      "id": 68,
      "difficulty": "hard",
      "question": "Radius=29 cm, chord length=40 cm. Find distance from center. 📐",
      "options": { "A": "20 cm", "B": "21 cm", "C": "22 cm", "D": "24 cm" },
      "correct_answer": "B"
    },
    {
      "id": 69,
      "difficulty": "hard",
      "question": "Chords intersect: PA=3, AB=15, PC=5, find CD. 🔍",
      "options": {
        "A": "7.2",
        "B": "6",
        "C": "8",
        "D": "10"
      },
      "correct_answer": "A"
    },
    {
      "id": 70,
      "difficulty": "hard",
      "question": "Two parallel chords on opposite sides: lengths 8 cm and 6 cm, distance between=7 cm. Find radius. 🔵",
      "options": { "A": "4 cm", "B": "5 cm", "C": "6 cm", "D": "7 cm" },
      "correct_answer": "B"
    },
    {
      "id": 71,
      "difficulty": "hard",
      "question": "Radius=34 cm, chord length=60 cm. Find distance from center. 📏",
      "options": { "A": "16 cm", "B": "20 cm", "C": "24 cm", "D": "30 cm" },
      "correct_answer": "A"
    },
    {
      "id": 72,
      "difficulty": "hard",
      "question": "Two chords intersect: segments 4,9 and 6,x. Find x. 🔍",
      "options": { "A": "4", "B": "5", "C": "6", "D": "7" },
      "correct_answer": "C"
    },
    {
      "id": 73,
      "difficulty": "hard",
      "question": "Chord=24 cm, distance=5 cm. Find radius. 📐",
      "options": { "A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm" },
      "correct_answer": "D"
    },
    {
      "id": 74,
      "difficulty": "hard",
      "question": "Two parallel chords 14 cm and 48 cm long are on same side, distance=17 cm. Find radius. 🔵",
      "options": { "A": "20 cm", "B": "25 cm", "C": "30 cm", "D": "35 cm" },
      "correct_answer": "B"
    },
    {
      "id": 75,
      "difficulty": "hard",
      "question": "Chords intersect: AE=6, EB=8, CE=12, find ED. 🔍",
      "options": { "A": "4", "B": "5", "C": "6", "D": "8" },
      "correct_answer": "A"
    },
    {
      "id": 76,
      "difficulty": "hard",
      "question": "Radius=25 cm, chord=14 cm. Find distance from center. 📏",
      "options": {
        "A": "21 cm",
        "B": "22 cm",
        "C": "23 cm",
        "D": "24 cm"
      },
      "correct_answer": "A"
    },
    {
      "id": 77,
      "difficulty": "hard",
      "question": "Two chords AB=10, CD=17 equidistant. Radius=13. Find distance. 🔍",
      "options": { "A": "10", "B": "11", "C": "12", "D": "13" },
      "correct_answer": "C"
    },
    {
      "id": 78,
      "difficulty": "hard",
      "question": "Chord=40 cm, distance=9 cm. Find radius. 📐",
      "options": { "A": "20 cm", "B": "21 cm", "C": "22 cm", "D": "25 cm" },
      "correct_answer": "B"
    },
    {
      "id": 79,
      "difficulty": "hard",
      "question": "Two intersecting chords: segments 5,7 and 10,x. Find x. 🔍",
      "options": { "A": "3.5", "B": "4", "C": "4.5", "D": "5" },
      "correct_answer": "A"
    },
    {
      "id": 80,
      "difficulty": "hard",
      "question": "Radius=15 cm, chord=18 cm. Find distance from center. 📏",
      "options": { "A": "9 cm", "B": "10 cm", "C": "12 cm", "D": "14 cm" },
      "correct_answer": "C"
    },
    {
      "id": 81,
      "difficulty": "hard",
      "question": "Two parallel chords 12 cm and 16 cm long on same side, 2 cm apart. Find radius. 🔵",
      "options": { "A": "8 cm", "B": "9 cm", "C": "10 cm", "D": "12 cm" },
      "correct_answer": "C"
    },
    {
      "id": 82,
      "difficulty": "hard",
      "question": "Chords intersect: PA=4, PB=16, PC=8, find PD. 🔍",
      "options": { "A": "4", "B": "6", "C": "8", "D": "10" },
      "correct_answer": "C"
    },
    {
      "id": 83,
      "difficulty": "hard",
      "question": "Radius=26 cm, chord=48 cm. Find distance. 📐",
      "options": { "A": "10 cm", "B": "12 cm", "C": "15 cm", "D": "20 cm" },
      "correct_answer": "A"
    },
    {
      "id": 84,
      "difficulty": "hard",
      "question": "Two chords equidistant: lengths 7 cm and 24 cm. Radius=12.5 cm. Find distance. 🔍",
      "options": { "A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm" },
      "correct_answer": "C"
    },
    {
      "id": 85,
      "difficulty": "hard",
      "question": "Chord=30 cm, distance=8 cm. Find radius. 📏",
      "options": { "A": "15 cm", "B": "17 cm", "C": "20 cm", "D": "25 cm" },
      "correct_answer": "B"
    },
    {
      "id": 86,
      "difficulty": "hard",
      "question": "Two intersecting chords: segments 2,8 and 4,x. Find x. 🔍",
      "options": { "A": "4", "B": "5", "C": "6", "D": "8" },
      "correct_answer": "A"
    },
    {
      "id": 87,
      "difficulty": "hard",
      "question": "Radius=10 cm, chord=12 cm. Find distance. 📐",
      "options": { "A": "6 cm", "B": "7 cm", "C": "8 cm", "D": "9 cm" },
      "correct_answer": "C"
    },
    {
      "id": 88,
      "difficulty": "hard",
      "question": "Two parallel chords 8 cm and 15 cm on opposite sides, 10 cm apart. Find radius. 🔵",
      "options": { "A": "8.5 cm", "B": "9 cm", "C": "9.5 cm", "D": "10 cm" },
      "correct_answer": "A"
    },
    {
      "id": 89,
      "difficulty": "hard",
      "question": "Chords intersect: AE=3, EB=12, CE=4, find ED. 🔍",
      "options": { "A": "9", "B": "10", "C": "12", "D": "15" },
      "correct_answer": "A"
    },
    {
      "id": 90,
      "difficulty": "hard",
      "question": "Radius=17 cm, chord=30 cm. Find distance. 📏",
      "options": { "A": "8 cm", "B": "10 cm", "C": "12 cm", "D": "15 cm" },
      "correct_answer": "A"
    },
    {
      "id": 91,
      "difficulty": "hard",
      "question": "Two chords AB=20, CD=48 equidistant. Radius=26. Find distance. 🔍",
      "options": { "A": "10", "B": "12", "C": "15", "D": "20" },
      "correct_answer": "A"
    },
    {
      "id": 92,
      "difficulty": "hard",
      "question": "Chord=32 cm, distance=12 cm. Find radius. 📐",
      "options": { "A": "18 cm", "B": "20 cm", "C": "22 cm", "D": "25 cm" },
      "correct_answer": "B"
    },
    {
      "id": 93,
      "difficulty": "hard",
      "question": "Two intersecting chords: segments 6,8 and 12,x. Find x. 🔍",
      "options": { "A": "4", "B": "5", "C": "6", "D": "8" },
      "correct_answer": "A"
    },
    {
      "id": 94,
      "difficulty": "hard",
      "question": "Radius=13 cm, chord=10 cm. Find distance. 📏",
      "options": { "A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm" },
      "correct_answer": "C"
    },
    {
      "id": 95,
      "difficulty": "hard",
      "question": "Two parallel chords 5 cm and 12 cm on same side, 3.5 cm apart. Find radius. 🔵",
      "options": { "A": "6.5 cm", "B": "7 cm", "C": "7.5 cm", "D": "8 cm" },
      "correct_answer": "A"
    },
    {
      "id": 96,
      "difficulty": "hard",
      "question": "Chords intersect: PA=5, PB=20, PC=10, find PD. 🔍",
      "options": { "A": "5", "B": "8", "C": "10", "D": "12" },
      "correct_answer": "C"
    },
    {
      "id": 97,
      "difficulty": "hard",
      "question": "Radius=37 cm, chord=70 cm. Find distance. 📐",
      "options": { "A": "12 cm", "B": "15 cm", "C": "20 cm", "D": "24 cm" },
      "correct_answer": "A"
    },
    {
      "id": 98,
      "difficulty": "hard",
      "question": "Two chords equidistant: lengths 9 cm and 40 cm. Radius=20.5 cm. Find distance. 🔍",
      "options": { "A": "15 cm", "B": "18 cm", "C": "20 cm", "D": "22 cm" },
      "correct_answer": "C"
    },
    {
      "id": 99,
      "difficulty": "hard",
      "question": "Chord=60 cm, distance=11 cm. Find radius. 📏",
      "options": { "A": "25 cm", "B": "30 cm", "C": "34 cm", "D": "36 cm" },
      "correct_answer": "C"
    },
    {
      "id": 100,
      "difficulty": "hard",
      "question": "Two intersecting chords: segments 7,9 and 21,x. Find x. 🔍",
      "options": { "A": "3", "B": "4", "C": "5", "D": "6" },
      "correct_answer": "A"
    }
  ]
}