{
  "title": "Arcs and Angles in Circles - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "The angle subtended by an arc at the center is ______ the angle subtended at any point on the remaining part of the circle.", "options": {"A": "equal to", "B": "half of", "C": "twice", "D": "four times"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "If arc AB subtends 60° at the center, the angle subtended by AB at any point on the major arc is:", "options": {"A": "30°", "B": "60°", "C": "120°", "D": "240°"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Angles in the same segment of a circle are:", "options": {"A": "equal", "B": "complementary", "C": "supplementary", "D": "none of these"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "The angle in a semicircle is always:", "options": {"A": "acute", "B": "right", "C": "obtuse", "D": "straight"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "If arc PQ subtends 40° at point R on the circle, it subtends ______ at the center.", "options": {"A": "20°", "B": "40°", "C": "80°", "D": "160°"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "Equal arcs subtend equal angles at the center. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. This is called:", "options": {"A": "Alternate segment theorem", "B": "Tangent chord theorem", "C": "Both A and B", "D": "None of these"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "If arc AB = arc CD, then chord AB ______ chord CD.", "options": {"A": "equals", "B": "is greater than", "C": "is less than", "D": "is parallel to"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "The angle subtended by a major arc at the center is:", "options": {"A": "acute", "B": "obtuse", "C": "reflex", "D": "right"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "If arc XY subtends 90° at the center, the angle subtended at any point on the minor arc is:", "options": {"A": "45°", "B": "90°", "C": "135°", "D": "180°"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "The sum of opposite angles of a cyclic quadrilateral is:", "options": {"A": "90°", "B": "180°", "C": "270°", "D": "360°"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "If an arc subtends θ at the center, it subtends ______ at any point on the remaining part.", "options": {"A": "θ/2", "B": "θ", "C": "2θ", "D": "180°-θ"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "An angle inscribed in a major arc is:", "options": {"A": "acute", "B": "right", "C": "obtuse", "D": "reflex"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "The angle between a radius and a tangent at the point of contact is:", "options": {"A": "45°", "B": "90°", "C": "180°", "D": "360°"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "If arc AB subtends 70° at point C on the circle, then arc AB measures:", "options": {"A": "35°", "B": "70°", "C": "140°", "D": "210°"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "Equal chords cut off equal arcs. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "The exterior angle of a cyclic quadrilateral is equal to:", "options": {"A": "adjacent interior angle", "B": "opposite interior angle", "C": "sum of opposite angles", "D": "difference of opposite angles"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "If an arc subtends 30° at the circumference, its measure is:", "options": {"A": "15°", "B": "30°", "C": "60°", "D": "90°"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "Angles in the same segment are equal because they are subtended by the same arc. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "The angle subtended by a diameter at any point on the circle is 90°. This is because the arc is a:", "options": {"A": "minor arc", "B": "major arc", "C": "semicircle", "D": "quadrant"}, "correct_answer": "C"},
    
    {"id": 21, "difficulty": "medium", "question": "In a circle with center O, arc AB subtends ∠AOB = 110°. Find angle subtended by arc AB at point C on the major arc.", "options": {"A": "55°", "B": "110°", "C": "125°", "D": "250°"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Arc PQ measures 80°. Find angle subtended by arc PQ at point R on the minor arc.", "options": {"A": "40°", "B": "80°", "C": "160°", "D": "280°"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "In a circle, arc AB subtends 50° at point C on the circle. Find measure of arc AB.", "options": {"A": "25°", "B": "50°", "C": "100°", "D": "200°"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "Arc CD measures 120°. Find angle subtended by arc CD at point E on the major arc.", "options": {"A": "60°", "B": "120°", "C": "240°", "D": "300°"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "In cyclic quadrilateral ABCD, ∠A = 70°. Find ∠C.", "options": {"A": "70°", "B": "110°", "C": "140°", "D": "290°"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Arc EF subtends 65° at point G on the minor arc. Find measure of arc EF.", "options": {"A": "32.5°", "B": "65°", "C": "130°", "D": "295°"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "Two arcs AB and CD are equal. If arc AB subtends 40° at center, find angle subtended by arc CD at any point on major arc.", "options": {"A": "20°", "B": "40°", "C": "80°", "D": "160°"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "In circle, arc GH measures 150°. Find angle subtended by arc GH at point I on the minor arc.", "options": {"A": "75°", "B": "150°", "C": "105°", "D": "30°"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "Arc JK subtends 55° at point L on the circle. Find angle subtended at center.", "options": {"A": "27.5°", "B": "55°", "C": "110°", "D": "125°"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "In cyclic quadrilateral PQRS, ∠P = 85°. Find ∠R.", "options": {"A": "85°", "B": "95°", "C": "175°", "D": "265°"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Arc MN measures 72°. Find angle subtended by arc MN at point O on the major arc.", "options": {"A": "36°", "B": "72°", "C": "108°", "D": "144°"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Two equal arcs subtend angles 35° and x° at circumference. Find x.", "options": {"A": "35°", "B": "70°", "C": "145°", "D": "215°"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Arc OP measures 160°. Find angle subtended by arc OP at point Q on the minor arc.", "options": {"A": "80°", "B": "160°", "C": "100°", "D": "20°"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "In circle, arc QR subtends 48° at point S. Find measure of arc QR.", "options": {"A": "24°", "B": "48°", "C": "96°", "D": "132°"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "In cyclic quadrilateral ABCD, ∠B = 105°. Find ∠D.", "options": {"A": "75°", "B": "105°", "C": "255°", "D": "285°"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Arc ST measures 92°. Find angle subtended by arc ST at point U on the major arc.", "options": {"A": "46°", "B": "92°", "C": "88°", "D": "268°"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Two arcs have measures in ratio 3:4. Angles subtended by them at circumference are in ratio:", "options": {"A": "3:4", "B": "4:3", "C": "9:16", "D": "√3:2"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Arc UV measures 142°. Find angle subtended by arc UV at point W on the minor arc.", "options": {"A": "71°", "B": "142°", "C": "109°", "D": "38°"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "Arc WX subtends 37° at point Y. Find angle subtended at center.", "options": {"A": "18.5°", "B": "37°", "C": "74°", "D": "143°"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "In cyclic quadrilateral PQRS, ∠Q = 115°. Find ∠S.", "options": {"A": "65°", "B": "115°", "C": "245°", "D": "295°"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Arc YZ measures 84°. Find angle subtended by arc YZ at point A on the major arc.", "options": {"A": "42°", "B": "84°", "C": "96°", "D": "276°"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Two equal arcs subtend angles x and 2x at center. This is:", "options": {"A": "possible", "B": "impossible", "C": "possible only if x=0", "D": "possible only if arcs are semicircles"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "Arc BC measures 168°. Find angle subtended by arc BC at point D on the minor arc.", "options": {"A": "84°", "B": "168°", "C": "96°", "D": "12°"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "Arc DE subtends 43° at point F. Find measure of arc DE.", "options": {"A": "21.5°", "B": "43°", "C": "86°", "D": "137°"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "In cyclic quadrilateral ABCD, ∠C = 95°. Find ∠A.", "options": {"A": "85°", "B": "95°", "C": "175°", "D": "265°"}, "correct_answer": "A"},
   {
  "id": 46,
  "difficulty": "medium",
  "question": "Arc FG measures 116°. Find angle subtended by arc FG at point H on the major arc.",
  "options": {"A": "58°", "B": "116°", "C": "122°", "D": "244°"},
  "correct_answer": "A"
}, {"id": 47, "difficulty": "medium", "question": "Arcs in ratio 5:6 subtend angles at circumference in ratio:", "options": {"A": "5:6", "B": "6:5", "C": "25:36", "D": "√5:√6"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Arc HI measures 152°. Find angle subtended by arc HI at point J on the minor arc.", "options": {"A": "76°", "B": "152°", "C": "104°", "D": "28°"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "medium", "question": "Arc JK subtends 59° at point L. Find angle subtended at center.", "options": {"A": "29.5°", "B": "59°", "C": "118°", "D": "121°"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "In cyclic quadrilateral PQRS, ∠R = 88°. Find ∠P.", "options": {"A": "88°", "B": "92°", "C": "178°", "D": "272°"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Arc LM measures 78°. Find angle subtended by arc LM at point N on the major arc.", "options": {"A": "39°", "B": "78°", "C": "102°", "D": "282°"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Two arcs have equal lengths but different radii. Angles subtended at centers are:", "options": {"A": "equal", "B": "inversely proportional to radii", "C": "directly proportional to radii", "D": "unrelated"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "Arc NO measures 136°. Find angle subtended by arc NO at point P on the minor arc.", "options": {"A": "68°", "B": "136°", "C": "112°", "D": "44°"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "Arc PQ subtends 61° at point R. Find measure of arc PQ.", "options": {"A": "30.5°", "B": "61°", "C": "122°", "D": "119°"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "In cyclic quadrilateral ABCD, ∠D = 102°. Find ∠B.", "options": {"A": "78°", "B": "102°", "C": "258°", "D": "282°"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Arc RS measures 148°. Find angle subtended by arc RS at point T on the major arc.", "options": {"A": "74°", "B": "148°", "C": "106°", "D": "32°"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "An arc subtends 30° at circumference. If radius is doubled, angle subtended at circumference by same arc length becomes:", "options": {"A": "15°", "B": "30°", "C": "60°", "D": "7.5°"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Arc TU measures 162°. Find angle subtended by arc TU at point V on the minor arc.", "options": {"A": "81°", "B": "162°", "C": "99°", "D": "18°"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "medium", "question": "Arc VW subtends 67° at point X. Find angle subtended at center.", "options": {"A": "33.5°", "B": "67°", "C": "134°", "D": "113°"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "In cyclic quadrilateral PQRS, ∠S = 78°. Find ∠Q.", "options": {"A": "78°", "B": "102°", "C": "258°", "D": "282°"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "Arc AB measures 94°. Find angle subtended by arc AB at point C on the major arc.", "options": {"A": "47°", "B": "94°", "C": "86°", "D": "274°"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "Two arcs of same circle subtend 40° and 80° at center. Their lengths are in ratio:", "options": {"A": "1:2", "B": "2:1", "C": "1:4", "D": "4:1"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Arc CD measures 176°. Find angle subtended by arc CD at point E on the minor arc.", "options": {"A": "88°", "B": "176°", "C": "92°", "D": "4°"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "Arc EF subtends 71° at point G. Find measure of arc EF.", "options": {"A": "35.5°", "B": "71°", "C": "142°", "D": "109°"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "In cyclic quadrilateral ABCD, ∠A = 83°. Find ∠C.", "options": {"A": "83°", "B": "97°", "C": "263°", "D": "277°"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "Arc GH measures 128°. Find angle subtended by arc GH at point I on the major arc.", "options": {"A": "64°", "B": "128°", "C": "116°", "D": "52°"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "An arc of length equal to radius subtends ______ radians at center. In degrees:", "options": {"A": "57.3°", "B": "60°", "C": "90°", "D": "180°"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "Arc IJ measures 144°. Find angle subtended by arc IJ at point K on the minor arc.", "options": {"A": "72°", "B": "144°", "C": "108°", "D": "36°"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "Arc KL subtends 73° at point M. Find angle subtended at center.", "options": {"A": "36.5°", "B": "73°", "C": "146°", "D": "107°"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "In cyclic quadrilateral PQRS, ∠R = 67°. Find ∠P.", "options": {"A": "67°", "B": "113°", "C": "247°", "D": "293°"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "Arc MN measures 106°. Find angle subtended by arc MN at point O on the major arc.", "options": {"A": "53°", "B": "106°", "C": "74°", "D": "254°"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "In a circle, arc length is proportional to:", "options": {"A": "radius", "B": "square of radius", "C": "central angle", "D": "both A and C"}, "correct_answer": "D"},
    {"id": 73, "difficulty": "medium", "question": "Arc OP measures 154°. Find angle subtended by arc OP at point Q on the minor arc.", "options": {"A": "77°", "B": "154°", "C": "103°", "D": "26°"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "Arc QR subtends 79° at point S. Find measure of arc QR.", "options": {"A": "39.5°", "B": "79°", "C": "158°", "D": "101°"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "In cyclic quadrilateral ABCD, ∠B = 112°. Find ∠D.", "options": {"A": "68°", "B": "112°", "C": "248°", "D": "292°"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Arc ST measures 138°. Find angle subtended by arc ST at point U on the major arc.", "options": {"A": "69°", "B": "138°", "C": "111°", "D": "42°"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "For a given arc length, angle subtended at center is inversely proportional to:", "options": {"A": "radius", "B": "diameter", "C": "both", "D": "neither"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "Arc UV measures 126°. Find angle subtended by arc UV at point W on the minor arc.", "options": {"A": "63°", "B": "126°", "C": "117°", "D": "54°"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "Arc WX subtends 81° at point Y. Find angle subtended at center.", "options": {"A": "40.5°", "B": "81°", "C": "162°", "D": "99°"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "In cyclic quadrilateral PQRS, ∠Q = 98°. Find ∠S.", "options": {"A": "82°", "B": "98°", "C": "262°", "D": "278°"}, "correct_answer": "A"},
    
    {"id": 81, "difficulty": "hard", "question": "In circle with center O, arcs AB and CD subtend angles 70° and 110° at O respectively. Find angle between chords AC and BD if they intersect at P.", "options": {"A": "20°", "B": "40°", "C": "60°", "D": "90°"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Two chords PQ and RS intersect at T inside circle. If arc PR = 100° and arc QS = 80°, find ∠PTR.", "options": {"A": "20°", "B": "40°", "C": "60°", "D": "90°"}, "correct_answer": "D"},
    {"id": 83, "difficulty": "hard", "question": "In circle, arc AB = 80°, arc BC = 100°, arc CD = 60°. Find ∠APC where P is intersection of chords AD and BC.", "options": {"A": "40°", "B": "60°", "C": "80°", "D": "100°"}, "correct_answer": "B"},
    {"id": 84, "difficulty": "hard", "question": "Chords EF and GH intersect at I. If arc EG = 110°, arc FH = 130°, find ∠EIH.", "options": {"A": "60°", "B": "80°", "C": "100°", "D": "120°"}, "correct_answer": "D"},
    {"id": 85, "difficulty": "hard", "question": "In cyclic quadrilateral ABCD, diagonals intersect at P. If ∠ABD = 30°, ∠DBC = 40°, find ∠APB.", "options": {"A": "50°", "B": "70°", "C": "110°", "D": "130°"}, "correct_answer": "C"},
    {"id": 86, "difficulty": "hard", "question": "Two chords JK and LM intersect at N. If arc JM = 120° and arc KL = 60°, find ∠JNL.", "options": {"A": "30°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "In circle, arcs in ratio 2:3:4 subtend angles at circumference that are in arithmetic progression. Find smallest arc.", "options": {"A": "40°", "B": "60°", "C": "80°", "D": "100°"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "Chords OP and QR intersect at S. If arc PR = 140°, arc OQ = 80°, find ∠OSR.", "options": {"A": "30°", "B": "50°", "C": "70°", "D": "110°"}, "correct_answer": "D"},
    {"id": 89, "difficulty": "hard", "question": "In cyclic quadrilateral, one diagonal divides it into two triangles. If arcs subtended by sides are 70°, 90°, 110°, find angles of quadrilateral.", "options": {"A": "70°,110°,90°,90°", "B": "80°,100°,80°,100°", "C": "85°,95°,85°,95°", "D": "75°,105°,75°,105°"}, "correct_answer": "B"},
    {"id": 90, "difficulty": "hard", "question": "Two chords ST and UV intersect at W. If arc SV = 150°, arc TU = 70°, find ∠SWU.", "options": {"A": "40°", "B": "60°", "C": "80°", "D": "110°"}, "correct_answer": "D"},
    {"id": 91, "difficulty": "hard", "question": "In circle, arcs AB, BC, CD are in ratio 3:4:5. If ∠AOD = 120°, find ∠ABC.", "options": {"A": "60°", "B": "75°", "C": "90°", "D": "105°"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "Chords XY and YZ are such that arc XZ = 160°. If ∠XYZ = 50°, find ∠XZY.", "options": {"A": "30°", "B": "50°", "C": "70°", "D": "80°"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "In cyclic quadrilateral, arcs between vertices are in ratio 1:2:3:4. Find largest angle of quadrilateral.", "options": {"A": "108°", "B": "120°", "C": "144°", "D": "150°"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "Two chords AB and CD intersect at E. If arc AC = 100°, arc BD = 120°, find ∠AEC.", "options": {"A": "50°", "B": "70°", "C": "110°", "D": "130°"}, "correct_answer": "C"},
    {"id": 95, "difficulty": "hard", "question": "In circle, arcs PQ, QR, RS are 80°, 100°, 120° respectively. If chords PS and QR intersect at T, find ∠PTR.", "options": {"A": "60°", "B": "80°", "C": "100°", "D": "120°"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "Chords LM and MN are such that arc LN = 140°. If ∠LMN = 60°, find ∠LNM.", "options": {"A": "40°", "B": "50°", "C": "70°", "D": "80°"}, "correct_answer": "D"},
    {"id": 97, "difficulty": "hard", "question": "In cyclic quadrilateral, sum of two opposite arcs is 240°. Find sum of other two arcs.", "options": {"A": "120°", "B": "240°", "C": "300°", "D": "360°"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "Two chords OP and QP intersect at P (on circle). If arc OQ = 130°, arc PQ = 90°, find ∠OPQ.", "options": {"A": "40°", "B": "50°", "C": "65°", "D": "70°"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "In circle, arcs AB, BC, CD, DA are in arithmetic progression with common difference 20°. Find ∠ABC.", "options": {"A": "80°", "B": "90°", "C": "100°", "D": "110°"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "Chords EF and FG are such that arc EG = 150°. If ∠EFG = 55°, find ∠EGF.", "options": {"A": "35°", "B": "55°", "C": "70°", "D": "75°"}, "correct_answer": "D"}
  ]
}