{
  "title": "Midpoint Theorem - Grade 9 Quadrilaterals",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "In triangle ABC, if D and E are midpoints of AB and AC, then DE is parallel to:", "options": {"A": "AB", "B": "AC", "C": "BC", "D": "None"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "In midpoint theorem, DE = ? of BC", "options": {"A": "Equal", "B": "Half", "C": "Double", "D": "One-third"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "If D and E are midpoints in triangle ABC, then DE ∥ BC and DE = ?", "options": {"A": "BC/2", "B": "BC/3", "C": "2BC", "D": "BC/4"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "In triangle, line joining midpoints of two sides is parallel to:", "options": {"A": "Third side", "B": "First side", "C": "Second side", "D": "Altitude"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "If D and E are midpoints of AB and AC in triangle ABC, what is DE:BC?", "options": {"A": "1:1", "B": "1:2", "C": "2:1", "D": "1:3"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Midpoint theorem applies to:", "options": {"A": "Any polygon", "B": "Triangle", "C": "Quadrilateral", "D": "Circle"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "If DE joins midpoints in triangle ABC, then quadrilateral DECB is:", "options": {"A": "Parallelogram", "B": "Trapezium", "C": "Rectangle", "D": "Square"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "In triangle PQR, S and T are midpoints of PQ and PR. ST = 5 cm. QR = ?", "options": {"A": "5 cm", "B": "10 cm", "C": "15 cm", "D": "20 cm"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "If line joining midpoints is 6 cm, third side is:", "options": {"A": "3 cm", "B": "6 cm", "C": "12 cm", "D": "18 cm"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "Midpoint theorem converse states: If line through midpoint of one side parallel to another side, it:", "options": {"A": "Bisects third side", "B": "Is equal to third side", "C": "Is perpendicular", "D": "Bisects angle"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "In triangle, line joining midpoints divides triangle into:", "options": {"A": "Two equal triangles", "B": "Two similar triangles", "C": "Four triangles", "D": "Trapezium and triangle"}, "correct_answer": "D"},
    {"id": 12, "difficulty": "easy", "question": "If D,E are midpoints of AB,AC in right triangle ABC right at A, then DE is:", "options": {"A": "Perpendicular to BC", "B": "Parallel to BC", "C": "Angle bisector", "D": "Median"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "Area of triangle formed by joining midpoints is ? of original", "options": {"A": "Half", "B": "One-fourth", "C": "One-third", "D": "Double"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "If BC = 14 cm in triangle ABC, and D,E are midpoints, then DE = ?", "options": {"A": "7 cm", "B": "14 cm", "C": "21 cm", "D": "28 cm"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "In equilateral triangle, line joining midpoints is ? to base", "options": {"A": "Parallel", "B": "Perpendicular", "C": "At 45°", "D": "At 60°"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "If DE joins midpoints and BC = 18, DE = ?", "options": {"A": "6", "B": "9", "C": "12", "D": "15"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Midpoint theorem is also called:", "options": {"A": "Basic proportionality theorem", "B": "Pythagoras theorem", "C": "Thales theorem", "D": "Apollonius theorem"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "If triangle sides are 6,8,10 and midpoints joined, perimeter of middle triangle:", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "D"},
    {"id": 19, "difficulty": "easy", "question": "Converse of midpoint theorem helps prove lines are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Equal", "D": "Bisectors"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "If D,E,F are midpoints of triangle ABC, then perimeter of DEF is ? of ABC", "options": {"A": "Half", "B": "One-fourth", "C": "One-third", "D": "Double"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "In triangle ABC, D and E are midpoints of AB and AC. If BC = 12 cm and ∠ABC = 60°, find DE length.", "options": {"A": "4 cm", "B": "5 cm", "C": "6 cm", "D": "7 cm"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "Triangle ABC has D,E,F as midpoints of BC,CA,AB. If perimeter of DEF = 15 cm, perimeter of ABC = ?", "options": {"A": "30 cm", "B": "45 cm", "C": "60 cm", "D": "75 cm"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "In quadrilateral ABCD, P,Q,R,S are midpoints of sides. PQRS is always:", "options": {"A": "Rectangle", "B": "Parallelogram", "C": "Rhombus", "D": "Square"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "In triangle ABC, D and E are midpoints of AB and AC. If DE = 3x-2 and BC = 5x+4, find x.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "Area of triangle formed by joining midpoints of triangle with area 48 cm² is:", "options": {"A": "12 cm²", "B": "16 cm²", "C": "20 cm²", "D": "24 cm²"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "In triangle ABC, line through D (midpoint of AB) parallel to BC meets AC at E. Then:", "options": {"A": "E is midpoint of AC", "B": "AE = EC", "C": "Both A and B", "D": "Neither"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "If midpoints of sides of quadrilateral are joined, area of inner quadrilateral is ? of original", "options": {"A": "Half", "B": "One-fourth", "C": "One-third", "D": "Two-thirds"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "In triangle ABC, D,E,F are midpoints. If AB=8, BC=10, CA=12, find perimeter of triangle DEF.", "options": {"A": "10", "B": "12", "C": "15", "D": "18"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "Triangle PQR has S,T as midpoints of PQ,PR. If ST = 6 cm and QR = 3x, find x.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "In right triangle ABC right at B, D,E are midpoints of AB,BC. Then DE is parallel to:", "options": {"A": "AB", "B": "BC", "C": "AC", "D": "None"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "If area of triangle formed by midpoints is 9 cm², area of original triangle:", "options": {"A": "18 cm²", "B": "27 cm²", "C": "36 cm²", "D": "45 cm²"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "In triangle ABC, D and E are midpoints. If DE = 7 cm and BC = (x+3) cm, find x.", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "Quadrilateral ABCD has midpoints P,Q,R,S. If ABCD is rectangle, PQRS is:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Parallelogram"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "In triangle ABC, line joining midpoints D and E is extended to meet line through C parallel to AB at F. Then ACFD is:", "options": {"A": "Parallelogram", "B": "Rectangle", "C": "Trapezium", "D": "Rhombus"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "If triangle sides are 12, 16, 20, perimeter of triangle joining midpoints:", "options": {"A": "12", "B": "18", "C": "24", "D": "30"}, "correct_answer": "C"},
    {"id": 36, "difficulty": "medium", "question": "In quadrilateral, lines joining midpoints of opposite sides:", "options": {"A": "Are equal", "B": "Bisect each other", "C": "Are perpendicular", "D": "Are parallel"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Triangle ABC has area 64. Triangle DEF formed by midpoints has area:", "options": {"A": "16", "B": "24", "C": "32", "D": "48"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "If D,E are midpoints of AB,AC and DE = 3x-1, BC = 8x+2, find x.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "In isosceles triangle ABC with AB=AC, D,E midpoints of AB,AC. Then quadrilateral BCED is:", "options": {"A": "Parallelogram", "B": "Isosceles trapezium", "C": "Rectangle", "D": "Rhombus"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "If midpoints of sides of rectangle are joined, resulting quadrilateral is:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Parallelogram"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "In triangle, line joining midpoints divides triangle into two parts with area ratio:", "options": {"A": "1:1", "B": "1:2", "C": "1:3", "D": "2:3"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "Triangle ABC ~ triangle DEF (midpoints). Scale factor is:", "options": {"A": "1:2", "B": "2:1", "C": "1:√2", "D": "√2:1"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "If quadrilateral ABCD is rhombus, quadrilateral formed by midpoints is:", "options": {"A": "Rectangle", "B": "Square", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "In triangle, line through midpoint of one side parallel to another side bisects:", "options": {"A": "Angle", "B": "Third side", "C": "Altitude", "D": "Median"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "If D,E,F are midpoints of triangle ABC, then triangle DEF ~ triangle ABC with ratio:", "options": {"A": "1:2", "B": "1:4", "C": "1:√2", "D": "2:1"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "In triangle ABC, D,E are midpoints. If BC = 14 and DE = 2x+1, find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "If quadrilateral formed by joining midpoints is square, original quadrilateral is:", "options": {"A": "Square", "B": "Rhombus", "C": "Rectangle", "D": "Parallelogram"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "medium", "question": "Area of quadrilateral formed by joining midpoints of quadrilateral of area 40 cm² is:", "options": {"A": "10 cm²", "B": "20 cm²", "C": "30 cm²", "D": "40 cm²"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "In triangle ABC, D,E are midpoints. If ∠ADE = 40°, then ∠ABC = ?", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "70°"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "If triangle sides are 13,14,15, sides of midpoint triangle are:", "options": {"A": "6.5,7,7.5", "B": "5,6,7", "C": "6,7,8", "D": "7,8,9"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "In quadrilateral ABCD, midpoints form parallelogram. Its diagonals are:", "options": {"A": "Half of AC and BD", "B": "Equal to AC and BD", "C": "Parallel to sides", "D": "Perpendicular"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Triangle ABC has D,E midpoints. If DE = 8 and BC = 4x, find x.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "If quadrilateral formed by midpoints is rectangle, original quadrilateral must have diagonals:", "options": {"A": "Equal", "B": "Perpendicular", "C": "Bisecting", "D": "Parallel"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "In triangle, segment joining midpoints is called:", "options": {"A": "Median", "B": "Midsegment", "C": "Altitude", "D": "Angle bisector"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "If area of midpoint triangle is 12, area of original:", "options": {"A": "24", "B": "36", "C": "48", "D": "60"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "In triangle ABC, D,E are midpoints. If AD = 5, then AB = ?", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "Quadrilateral formed by joining midpoints of square is:", "options": {"A": "Square", "B": "Rhombus", "C": "Rectangle", "D": "Parallelogram"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "If triangle perimeter is 30, perimeter of midpoint triangle:", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "In triangle ABC, D,E,F midpoints. Area of triangle DEF : Area triangle ABC = ?", "options": {"A": "1:2", "B": "1:3", "C": "1:4", "D": "2:3"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "If quadrilateral ABCD has AC⟂BD, quadrilateral formed by midpoints is:", "options": {"A": "Rectangle", "B": "Square", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "In triangle, line through midpoint parallel to base creates trapezium with area ? of triangle", "options": {"A": "Half", "B": "One-third", "C": "Three-fourths", "D": "Two-thirds"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "Triangle sides: 9,12,15. Midpoint triangle sides:", "options": {"A": "3,4,5", "B": "4.5,6,7.5", "C": "5,6,7", "D": "6,8,10"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "If quadrilateral formed by midpoints is rhombus, original quadrilateral has:", "options": {"A": "Equal sides", "B": "Equal diagonals", "C": "Perpendicular diagonals", "D": "All sides equal"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "In triangle ABC, D,E midpoints. If BC = 16, DE = ?", "options": {"A": "4", "B": "6", "C": "8", "D": "10"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "Area ratio of four triangles formed by joining midpoints to original triangle:", "options": {"A": "1:1:1:1", "B": "1:2:2:1", "C": "1:1:2:2", "D": "1:2:1:2"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "If quadrilateral ABCD has AC=BD, quadrilateral by midpoints is:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Parallelogram"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "In triangle, midsegment is ? of base in length", "options": {"A": "Equal", "B": "Half", "C": "Double", "D": "One-fourth"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "Triangle ABC has area 36. Area of quadrilateral formed by midpoints D,E and vertices B,C:", "options": {"A": "12", "B": "18", "C": "24", "D": "27"}, "correct_answer": "D"},
    {"id": 69, "difficulty": "medium", "question": "If quadrilateral formed by midpoints is parallelogram, its diagonals are parallel to:", "options": {"A": "Sides of original", "B": "Diagonals of original", "C": "Nothing specific", "D": "Each other"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "In right triangle, midsegment to hypotenuse is ? in length", "options": {"A": "Half of hypotenuse", "B": "Equal to hypotenuse", "C": "One-fourth hypotenuse", "D": "√2 times hypotenuse"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "If triangle sides are a,b,c, sides of midpoint triangle:", "options": {"A": "a/2, b/2, c/2", "B": "a/3, b/3, c/3", "C": "2a, 2b, 2c", "D": "a/4, b/4, c/4"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Quadrilateral ABCD has P,Q,R,S midpoints. Then PR and QS:", "options": {"A": "Are equal", "B": "Bisect each other", "C": "Are perpendicular", "D": "Are parallel"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "In triangle, if midsegment = 6, base = ?", "options": {"A": "3", "B": "6", "C": "9", "D": "12"}, "correct_answer": "D"},
    {"id": 74, "difficulty": "medium", "question": "If quadrilateral formed by midpoints is square, original quadrilateral diagonals are:", "options": {"A": "Equal and perpendicular", "B": "Only equal", "C": "Only perpendicular", "D": "Neither equal nor perpendicular"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Triangle ABC ~ DEF (midpoints). Ratio of corresponding altitudes:", "options": {"A": "1:2", "B": "2:1", "C": "1:1", "D": "1:√2"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "In triangle, line joining midpoints divides median in ratio:", "options": {"A": "1:1", "B": "1:2", "C": "2:1", "D": "1:3"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "If quadrilateral ABCD is parallelogram, quadrilateral by midpoints is:", "options": {"A": "Parallelogram", "B": "Rectangle", "C": "Rhombus", "D": "Square"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "In triangle ABC, D,E midpoints. If ∠BAC = 50°, then ∠DAE = ?", "options": {"A": "25°", "B": "50°", "C": "75°", "D": "100°"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "Area of four triangles formed by joining midpoints are:", "options": {"A": "All equal", "B": "Two pairs equal", "C": "All different", "D": "Three equal, one different"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "If midsegment = 2x+3 and base = 6x-1, find x.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    
    {"id": 81, "difficulty": "hard", "question": "In triangle ABC, D,E,F are midpoints. If area of triangle DEF = 6 cm², area of quadrilateral ADFE = ?", "options": {"A": "12 cm²", "B": "18 cm²", "C": "24 cm²", "D": "30 cm²"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "Quadrilateral ABCD has diagonals AC=12, BD=16 at 60°. Area of quadrilateral formed by midpoints:", "options": {"A": "24√3", "B": "36√3", "C": "48√3", "D": "64√3"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Triangle ABC has sides AB=13, BC=14, CA=15. D,E are midpoints of AB,AC. Find DE.", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "B"},
    {"id": 84, "difficulty": "hard", "question": "In quadrilateral ABCD, P,Q,R,S are midpoints. If PR=10, QS=8, then AC²+BD² = ?", "options": {"A": "164", "B": "180", "C": "200", "D": "224"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "Triangle ABC has area 48. D,E,F are midpoints. Area of triangle AFE = ?", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "D"},
    {"id": 86, "difficulty": "hard", "question": "In triangle ABC, D,E are midpoints of AB,AC. If BC=10 and DE=6, triangle is:", "options": {"A": "Right triangle", "B": "Isosceles", "C": "Equilateral", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Quadrilateral ABCD has vertices (0,0), (4,0), (6,3), (2,3). Area of quadrilateral formed by midpoints:", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "Triangle ABC ~ triangle DEF (midpoints). If perimeter of ABC = 36 and area = 48, perimeter and area of DEF:", "options": {"A": "18, 12", "B": "18, 24", "C": "24, 12", "D": "24, 24"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "In quadrilateral ABCD, midpoints form rectangle with sides 6 and 8. If one diagonal of ABCD is 20, other diagonal:", "options": {"A": "10", "B": "12", "C": "14", "D": "16"}, "correct_answer": "B"},
    {"id": 90, "difficulty": "hard", "question": "Triangle ABC has medians AD,BE,CF intersecting at G. If D,E,F are midpoints of sides, then area(GDEF):area(ABC) = ?", "options": {"A": "1:6", "B": "1:9", "C": "1:12", "D": "1:18"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "In triangle ABC, D,E,F are midpoints. If AB=8, BC=10, CA=12, and G is centroid, find area of triangle GDE.", "options": {"A": "√15", "B": "2√15", "C": "3√15", "D": "4√15"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "Quadrilateral ABCD has area 60. Lines through midpoints parallel to diagonals form parallelogram with area:", "options": {"A": "15", "B": "20", "C": "30", "D": "40"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "Triangle ABC has sides 7,24,25. Area of triangle formed by joining midpoints:", "options": {"A": "21", "B": "42", "C": "63", "D": "84"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "In quadrilateral ABCD, P,Q,R,S midpoints. If ABCD is cyclic, then PQRS is:", "options": {"A": "Cyclic", "B": "Rectangle", "C": "Rhombus", "D": "Square"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "Triangle ABC has area 72. D,E,F are midpoints. Lines through vertices parallel to opposite sides form triangle with area:", "options": {"A": "144", "B": "216", "C": "288", "D": "360"}, "correct_answer": "C"},
    {"id": 96, "difficulty": "hard", "question": "In quadrilateral ABCD, midpoints form rhombus with side 5. If one diagonal of ABCD is 12, area of ABCD:", "options": {"A": "48", "B": "60", "C": "72", "D": "96"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "Triangle ABC has vertices A(0,0), B(6,0), C(3,4). Area of triangle formed by midpoints:", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "Quadrilateral ABCD has diagonals perpendicular. If AC=8, BD=6, area of quadrilateral formed by midpoints:", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "In triangle ABC, D,E,F are midpoints. If triangle DEF is equilateral with side 4, area of triangle ABC:", "options": {"A": "8√3", "B": "12√3", "C": "16√3", "D": "20√3"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "Quadrilateral ABCD has P,Q,R,S midpoints. If PQRS is square with side 6, then AC²+BD² = ?", "options": {"A": "72", "B": "96", "C": "144", "D": "288"}, "correct_answer": "D"}
  ]
}