{
  "title": "Properties of Quadrilaterals (Rectilinear Figures) - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "How many sides does a quadrilateral have? 🔢", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "Sum of interior angles of any quadrilateral is: 📐", "options": {"A": "180°", "B": "270°", "C": "360°", "D": "450°"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "A quadrilateral with all sides equal but angles not 90° is: 🔶", "options": {"A": "Square", "B": "Rectangle", "C": "Rhombus", "D": "Trapezium"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "Which quadrilateral has exactly one pair of parallel sides? 📏", "options": {"A": "Parallelogram", "B": "Rhombus", "C": "Trapezium", "D": "Kite"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "In a kite, diagonals are: ✖️", "options": {"A": "Equal", "B": "Perpendicular", "C": "Parallel", "D": "None"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Rectangle has all angles equal to: ⬛", "options": {"A": "60°", "B": "90°", "C": "120°", "D": "180°"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "A square is both a rectangle and a: 💎", "options": {"A": "Trapezium", "B": "Kite", "C": "Rhombus", "D": "None"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "If three angles of quadrilateral are 80°, 90°, 100°, fourth angle is: 🔢", "options": {"A": "70°", "B": "80°", "C": "90°", "D": "100°"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "Quadrilateral with both pairs of opposite sides parallel is: 🔄", "options": {"A": "Kite", "B": "Trapezium", "C": "Parallelogram", "D": "Cyclic"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "Diagonals of square are: ⬛", "options": {"A": "Equal and bisect at right angles", "B": "Unequal", "C": "Not perpendicular", "D": "None"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "In a cyclic quadrilateral, opposite angles are: 🔄", "options": {"A": "Equal", "B": "Supplementary", "C": "Complementary", "D": "Right"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "A quadrilateral with two distinct pairs of equal adjacent sides is: 🪁", "options": {"A": "Parallelogram", "B": "Rhombus", "C": "Kite", "D": "Trapezium"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "Diagonals of rhombus bisect each other at: 📐", "options": {"A": "Acute angles", "B": "Right angles", "C": "Obtuse angles", "D": "180°"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Which quadrilateral's diagonals are equal? ⚖️", "options": {"A": "Rhombus", "B": "Kite", "C": "Rectangle", "D": "Parallelogram"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "Sum of exterior angles of quadrilateral is: 🔄", "options": {"A": "180°", "B": "270°", "C": "360°", "D": "540°"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "Isosceles trapezium has: 📏", "options": {"A": "Non-parallel sides equal", "B": "Parallel sides equal", "C": "All sides equal", "D": "Right angles"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "In parallelogram, diagonals: ✖️", "options": {"A": "Are equal", "B": "Bisect each other", "C": "Are perpendicular", "D": "Bisect angles"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "Quadrilateral with all sides equal and all angles 90° is: ⬛", "options": {"A": "Rhombus", "B": "Square", "C": "Rectangle", "D": "Kite"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "A quadrilateral is a parallelogram if: ✅", "options": {"A": "Opposite sides equal", "B": "Opposite angles equal", "C": "Diagonals bisect", "D": "Any one of these"}, "correct_answer": "D"},
    {"id": 20, "difficulty": "easy", "question": "Angles of quadrilateral are in ratio 1:2:3:4. Largest angle is: 🔢", "options": {"A": "144°", "B": "120°", "C": "108°", "D": "90°"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "If angles of quadrilateral are (2x)°, (3x+10)°, (4x-30)°, (x+40)°, find smallest angle. 📐", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "Diagonals of rectangle ABCD intersect at O. If ∠AOB = 110°, find ∠OAD. 🔄", "options": {"A": "35°", "B": "45°", "C": "55°", "D": "65°"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "In kite PQRS, PQ=QR=13 cm, PS=RS=20 cm, diagonal PR=24 cm. Find QS. 🪁", "options": {"A": "10 cm", "B": "12 cm", "C": "14 cm", "D": "16 cm"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Quadrilateral ABCD is cyclic with ∠A=70°, ∠B=120°. Find ∠D. 🔄", "options": {"A": "60°", "B": "70°", "C": "80°", "D": "90°"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "In trapezium, parallel sides are 12 and 18 cm, non-parallel sides 7 and 9 cm. Find height. 📏", "options": {"A": "5 cm", "B": "6 cm", "C": "7 cm", "D": "8 cm"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Diagonals of quadrilateral bisect each other at right angles but are unequal. Shape is: 🔷", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Kite"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "If one interior angle of quadrilateral is 135°, its exterior angle is: 🔄", "options": {"A": "35°", "B": "45°", "C": "55°", "D": "65°"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "In cyclic quadrilateral ABCD, ∠A:∠C=3:7. Find ∠C. 🔄", "options": {"A": "105°", "B": "126°", "C": "144°", "D": "162°"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "Parallelogram with vertices (0,0), (a,0), (a+b,c), (b,c) has area = ? 📊", "options": {"A": "ac", "B": "bc", "C": "ab", "D": "(a+b)c"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "In rhombus, diagonals are 16 and 30 cm. Find side length. 💎", "options": {"A": "17 cm", "B": "18 cm", "C": "19 cm", "D": "20 cm"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Quadrilateral with sides 5,12,14,15 cm. If sum of opposite angles 180°, find area (approx). 📊", "options": {"A": "80 cm²", "B": "90 cm²", "C": "100 cm²", "D": "110 cm²"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "In rectangle, diagonal is 26 cm, one side is 10 cm. Find perimeter. 📏", "options": {"A": "68 cm", "B": "72 cm", "C": "76 cm", "D": "80 cm"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Isosceles trapezium ABCD, AB||CD, AB=10, CD=6, equal sides=5. Find height. 📐", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "In parallelogram, one angle is 30° more than twice adjacent angle. Find angles. 🔢", "options": {"A": "50°,130°", "B": "60°,120°", "C": "70°,110°", "D": "80°,100°"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "Quadrilateral with vertices A(1,1), B(4,5), C(9,5), D(6,1). Type is: 🔷", "options": {"A": "Parallelogram", "B": "Rhombus", "C": "Rectangle", "D": "Kite"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Diagonals of kite are 12 and 16 cm. Area = ? 🪁", "options": {"A": "96 cm²", "B": "100 cm²", "C": "104 cm²", "D": "108 cm²"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "In cyclic quadrilateral, ∠A=2x+10, ∠B=3x+20, ∠C=4x-30, ∠D=5x-40. Find ∠D. 🔄", "options": {"A": "100°", "B": "110°", "C": "120°", "D": "130°"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "Quadrilateral ABCD has AB=BC=CD, ∠B=90°, ∠C=150°. Find ∠D. 📐", "options": {"A": "60°", "B": "75°", "C": "90°", "D": "105°"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "Midpoints of sides of quadrilateral form a rectangle. Original quadrilateral must have: 🔲", "options": {"A": "Equal sides", "B": "Perpendicular diagonals", "C": "Equal diagonals", "D": "Parallel sides"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "In quadrilateral, sum of three angles is 300°. Fourth angle is: 📐", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "hard", "question": "In cyclic quadrilateral ABCD, AB=4, BC=5, CD=6, DA=7. Find diagonal AC. 🔄", "options": {"A": "√30", "B": "√35", "C": "√40", "D": "√45"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "Quadrilateral with sides a,b,c,d is cyclic. If sides in order 7,8,9,d and area max when d=? 📐", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "Diagonals of quadrilateral ABCD intersect at 90°. Given AB=10, BC=15, CD=12, DA=9. Find area. 📊", "options": {"A": "108", "B": "114", "C": "120", "D": "126"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "hard", "question": "In convex quadrilateral, sum of distances from any interior point to sides is constant if: ⚖️", "options": {"A": "It is parallelogram", "B": "It is rhombus", "C": "It is tangential", "D": "Never constant"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "hard", "question": "Quadrilateral ABCD circumscribes circle with AB=8, BC=12, CD=10. Find AD. 🔄", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "In trapezium ABCD, AB||DC, E on AD, F on BC such that AE:ED=BF:FC=2:3. EF divides area in ratio? 📊", "options": {"A": "2:3", "B": "3:2", "C": "4:5", "D": "5:4"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "Quadrilateral with sides 6,7,8,9 cm has one diagonal 10 cm. Find length of other diagonal. ⚖️", "options": {"A": "√105", "B": "√111", "C": "√117", "D": "√123"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "hard", "question": "Cyclic quadrilateral's sides are 5,6,7,8 cm. Find radius of circumcircle. 🔵", "options": {"A": "√(210/31)", "B": "√(310/41)", "C": "√(410/51)", "D": "√(510/61)"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "In quadrilateral ABCD, ∠A+∠C=180°, AB=5, BC=12, CD=14, DA=9. Find area. 📊", "options": {"A": "60", "B": "66", "C": "72", "D": "78"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "Diagonals of quadrilateral are perpendicular. Sides are 6,9,12,15. Find area. 📐", "options": {"A": "90", "B": "96", "C": "102", "D": "108"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "hard", "question": "Tangential quadrilateral has sides 7,8,9,10. Find inradius. 🔵", "options": {"A": "√5", "B": "√6", "C": "√7", "D": "√8"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "hard", "question": "In parallelogram ABCD, P on AB divides AP:PB=2:3, Q on CD divides CQ:QD=3:2. PQ divides diagonal BD in ratio? 🔄", "options": {"A": "2:3", "B": "3:2", "C": "1:1", "D": "4:1"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "hard", "question": "Cyclic quadrilateral's diagonals are 8 and 10, and include angle 60°. Find area. 📊", "options": {"A": "20√3", "B": "25√3", "C": "30√3", "D": "35√3"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "In quadrilateral, midpoints of sides form rhombus. Original quadrilateral must have: 💎", "options": {"A": "Equal sides", "B": "Equal diagonals", "C": "Perpendicular diagonals", "D": "Diagonals bisect angles"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "Quadrilateral ABCD has AB=CD, ∠B=∠C=90°, AD=13, BC=10. Find AB. 📏", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "hard", "question": "In trapezium, parallel sides 10 and 20, other sides 13 and 14. Find area. 📊", "options": {"A": "144", "B": "156", "C": "168", "D": "180"}, "correct_answer": "D"},
    {"id": 57, "difficulty": "hard", "question": "In convex quadrilateral, sum of squares of sides equals sum of squares of diagonals plus 4×(d₁d₂cosθ). θ is angle between diagonals? 📐", "options": {"A": "Yes, always", "B": "Only if cyclic", "C": "Only if parallelogram", "D": "Never"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "Quadrilateral with vertices (0,0), (6,0), (4,4), (0,3) has area? 📊", "options": {"A": "15", "B": "16", "C": "17", "D": "18"}, "correct_answer": "D"},
    {"id": 59, "difficulty": "hard", "question": "Tangential quadrilateral has area 100 and inradius 5. Find perimeter. 📏", "options": {"A": "30", "B": "35", "C": "40", "D": "45"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "hard", "question": "In cyclic quadrilateral ABCD, ∠A=60°, AB=3, AD=4. If diagonal BD=5, find BC. 🔄", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"}
  ]
}