{
  "title": "Construction of Triangles - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Which instrument is essential for constructing triangles?", "options": {"A": "Protractor", "B": "Divider", "C": "Ruler and compasses", "D": "Set square"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "To construct a triangle with sides 5cm, 6cm, 7cm, which property must be satisfied?", "options": {"A": "Sum of two sides < third side", "B": "Sum of two sides > third side", "C": "Difference of two sides > third side", "D": "All sides equal"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "How many measurements are needed to construct a unique triangle?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "For constructing ΔABC with AB=4cm, BC=5cm, ∠B=60°, which side is drawn first?", "options": {"A": "AB", "B": "BC", "C": "AC", "D": "Any side"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "What type of triangle is constructed when all three sides are equal?", "options": {"A": "Isosceles", "B": "Scalene", "C": "Equilateral", "D": "Right angled"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "To construct ΔPQR with PQ=5cm, QR=7cm, PR=9cm, what is the first step?", "options": {"A": "Draw QR=7cm", "B": "Draw PQ=5cm", "C": "Draw PR=9cm", "D": "Draw any line"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "When constructing ΔXYZ with XY=6cm, ∠X=50°, ∠Y=70°, the third angle measures:", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "Which triangle cannot be constructed with sides 3cm, 4cm, 8cm?", "options": {"A": "Because 3+4<8", "B": "Because 4+8<3", "C": "Because 3+8<4", "D": "All sides valid"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "For SSS construction, how many arcs are drawn from endpoints of base?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "In ASA construction, which elements are given?", "options": {"A": "Two angles and included side", "B": "Two sides and included angle", "C": "Three sides", "D": "Two angles and non-included side"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "What is the sum of angles in any triangle?", "options": {"A": "90°", "B": "180°", "C": "270°", "D": "360°"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "In RHS construction, the right angle is between:", "options": {"A": "Hypotenuse and any side", "B": "Two legs", "C": "Any two sides", "D": "Not specified"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "For constructing equilateral triangle with side 5cm, each angle measures:", "options": {"A": "45°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Which case requires constructing an angle first?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "When two sides and included angle are given, it's called:", "options": {"A": "SSS criterion", "B": "SAS criterion", "C": "ASA criterion", "D": "RHS criterion"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "To construct triangle with base 6cm and base angles 45° each, it will be:", "options": {"A": "Equilateral", "B": "Isosceles", "C": "Scalene", "D": "Right angled"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "What instrument measures angles in construction?", "options": {"A": "Ruler", "B": "Compass", "C": "Protractor", "D": "Divider"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "In ΔABC construction with AB=7cm, BC=8cm, CA=9cm, which side is longest?", "options": {"A": "AB", "B": "BC", "C": "CA", "D": "All equal"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "How many triangles can be constructed with sides 5cm, 5cm, 5cm?", "options": {"A": "0", "B": "1", "C": "2", "D": "Infinite"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "Triangle with sides 7cm, 24cm, 25cm is:", "options": {"A": "Acute", "B": "Obtuse", "C": "Right angled", "D": "Equilateral"}, "correct_answer": "C"},
    {"id": 21, "difficulty": "medium", "question": "Construct ΔPQR where PQ=6cm, ∠P=60°, ∠Q=45°. What is the measure of ∠R?", "options": {"A": "60°", "B": "65°", "C": "70°", "D": "75°"}, "correct_answer": "D"},
    {"id": 22, "difficulty": "medium", "question": "Construct ΔABC with BC=7cm, ∠B=75°, AB+AC=13cm. What type of construction is this?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "Sum of two sides given"}, "correct_answer": "D"},
    {"id": 23, "difficulty": "medium", "question": "Construct right triangle ABC, right angled at B with BC=4cm, AC=5cm. What is length of AB?", "options": {"A": "2cm", "B": "3cm", "C": "4cm", "D": "5cm"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "Construct isosceles triangle with base 8cm and each base angle 65°. What is vertex angle?", "options": {"A": "40°", "B": "45°", "C": "50°", "D": "55°"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "Construct ΔXYZ where XY=5cm, YZ=6cm, ∠Y=120°. Which angle will be largest?", "options": {"A": "∠X", "B": "∠Y", "C": "∠Z", "D": "All equal"}, "correct_answer": "B"},
   {"id": 26, "difficulty": "medium", "question": "Construct triangle with perimeter 15cm and sides in ratio 2:3:4. What is longest side?", "options": {"A": "20/3 cm", "B": "6 cm", "C": "20/3 ≈ 6.67cm", "D": "7 cm"}, "correct_answer": "A"},  {"id": 27, "difficulty": "medium", "question": "Construct ΔPQR with PQ=7cm, QR=8cm, PR=9cm. Arrange angles in ascending order:", "options": {"A": "∠P<∠Q<∠R", "B": "∠Q<∠R<∠P", "C": "∠R<∠P<∠Q", "D": "∠P<∠R<∠Q"}, "correct_answer": "C"},   {"id": 28, "difficulty": "medium", "question": "Construct triangle with sides 5cm, 12cm, 13cm. What type of triangle is formed?", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Equilateral"}, "correct_answer": "B"},
   {"id": 29, "difficulty": "medium", "question": "Construct ΔABC with AB=6cm, BC=5cm, CA=7cm. What is approximate difference between largest and smallest angles?", "options": {"A": "20°", "B": "30°", "C": "34°", "D": "40°"}, "correct_answer": "C"},    {"id": 30, "difficulty": "medium", "question": "Construct equilateral triangle of side 6cm. What is its altitude?", "options": {"A": "3√2 cm", "B": "3√3 cm", "C": "4√2 cm", "D": "4√3 cm"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Construct ΔLMN with LM=5.5cm, ∠L=60°, ∠M=45°. What is length of side opposite 45°?", "options": {"A": "4.5cm", "B": "5.0cm", "C": "5.5cm", "D": "6.0cm"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "Construct triangle with angles 50°, 60°, 70°. How many such triangles can be drawn?", "options": {"A": "0", "B": "1", "C": "2", "D": "Infinite"}, "correct_answer": "D"},
    {"id": 33, "difficulty": "medium", "question": "Construct right isosceles triangle with equal sides 5cm each. What is hypotenuse?", "options": {"A": "5cm", "B": "5√2 cm", "C": "10cm", "D": "10√2 cm"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "Construct ΔABC with AB=8cm, AC=10cm, ∠A=30°. What is length of BC approximately?", "options": {"A": "5.0cm", "B": "5.5cm", "C": "6.0cm", "D": "6.5cm"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Construct triangle with sides 7cm, 8cm, and included angle 45°. What is area formula?", "options": {"A": "½×7×8", "B": "½×7×8×sin45°", "C": "7×8×sin45°", "D": "½×7×8×cos45°"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Construct scalene triangle with sides 4.5cm, 6cm, 7.5cm. What type of triangle?", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Equilateral"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Construct ΔPQR with ∠P=55°, ∠Q=65°, PQ=7cm. What is length of side opposite largest angle?", "options": {"A": "QR", "B": "PR", "C": "PQ", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Construct triangle with vertices A(0,0), B(4,0), C(0,3). What is its area?", "options": {"A": "6 sq units", "B": "12 sq units", "C": "24 sq units", "D": "36 sq units"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Construct triangle where two angles are 40° and 80°. What is third angle?", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "70°"}, "correct_answer": "C"},
   {"id": 40, "difficulty": "medium", "question": "Construct ΔABC with AB=5cm, BC=6cm, ∠B=90°. What is length of median to hypotenuse?", "options": {"A": "√61/2 cm", "B": "3.0cm", "C": "3.5cm", "D": "4.0cm"}, "correct_answer": "A"},    {"id": 41, "difficulty": "medium", "question": "Construct triangle with base 10cm and base angles 30° and 60°. What is height?", "options": {"A": "5cm", "B": "5√3 cm", "C": "10cm", "D": "10√3 cm"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Construct ΔXYZ with XY=8cm, YZ=15cm, XZ=17cm. Which angle is right angle?", "options": {"A": "∠X", "B": "∠Y", "C": "∠Z", "D": "No right angle"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "Construct triangle with sides in ratio 3:4:5 and perimeter 24cm. What is longest side?", "options": {"A": "6cm", "B": "8cm", "C": "10cm", "D": "12cm"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "Construct ΔABC with AB=7cm, ∠A=45°, ∠B=75°. What is length of AC approximately?", "options": {"A": "8.5cm", "B": "9.1cm", "C": "9.6cm", "D": "10.2cm"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "Construct isosceles right triangle with hypotenuse 10cm. What are equal sides?", "options": {"A": "5cm", "B": "5√2 cm", "C": "10cm", "D": "10√2 cm"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "medium", "question": "Construct triangle with vertices on circle of radius 5cm forming 60° at center. What type?", "options": {"A": "Equilateral", "B": "Isosceles", "C": "Scalene", "D": "Right"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Construct ΔPQR with PQ=6cm, QR=7cm, ∠Q=30°. What is area approximately?", "options": {"A": "10.5 sq cm", "B": "12.0 sq cm", "C": "13.5 sq cm", "D": "15.0 sq cm"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Construct triangle with sides 9cm, 12cm, 15cm. What is radius of circumcircle?", "options": {"A": "6.5cm", "B": "7.5cm", "C": "8.5cm", "D": "9.5cm"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "Construct ΔABC with BC=8cm, ∠B=60°, AB-AC=3cm. What is length AB?", "options": {"A": "9cm", "B": "10cm", "C": "11cm", "D": "12cm"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "Construct triangle with two sides 8cm, 11cm and perimeter 30cm. What is third side?", "options": {"A": "9cm", "B": "10cm", "C": "11cm", "D": "12cm"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "medium", "question": "Construct ΔXYZ with XY=5cm, ∠X=50°, XZ=7cm. How many triangles possible?", "options": {"A": "0", "B": "1", "C": "2", "D": "Infinite"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "Construct triangle with angles 45°, 45°, 90°. What is side ratio?", "options": {"A": "1:1:1", "B": "1:1:√2", "C": "1:√2:√3", "D": "1:2:√3"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "Construct ΔABC with AB=9cm, BC=12cm, ∠B=120°. What is AC approximately?", "options": {"A": "15.8cm", "B": "17.3cm", "C": "18.6cm", "D": "19.2cm"}, "correct_answer": "D"},
    {"id": 54, "difficulty": "medium", "question": "Construct triangle with medians 6cm, 8cm, 10cm. What type?", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Cannot construct"}, "correct_answer": "D"},
    {"id": 55, "difficulty": "medium", "question": "Construct ΔPQR with PQ=PR=10cm, QR=12cm. What is altitude from P?", "options": {"A": "6cm", "B": "8cm", "C": "10cm", "D": "12cm"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "Construct triangle with two angles 55°, 55°. What type?", "options": {"A": "Equilateral", "B": "Isosceles", "C": "Scalene", "D": "Right"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "Construct ΔABC with ∠A=90°, AB=3cm, AC=4cm. What is BC?", "options": {"A": "4cm", "B": "5cm", "C": "6cm", "D": "7cm"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "medium", "question": "Construct triangle with vertices A(2,3), B(5,7), C(9,4). What is perimeter approximately?", "options": {"A": "15 units", "B": "18 units", "C": "21 units", "D": "24 units"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "Construct ΔXYZ with XY=6cm, ∠X=30°, ∠Y=100°. What is ∠Z?", "options": {"A": "30°", "B": "40°", "C": "50°", "D": "60°"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "Construct triangle with sides 6cm, 8cm, 10cm. What is area?", "options": {"A": "24 sq cm", "B": "30 sq cm", "C": "36 sq cm", "D": "48 sq cm"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "Construct ΔABC with AB=5cm, AC=7cm, BC=8cm. What is smallest angle?", "options": {"A": "∠A", "B": "∠B", "C": "∠C", "D": "All equal"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "Construct isosceles triangle with equal sides 13cm, base 10cm. What is area?", "options": {"A": "60 sq cm", "B": "65 sq cm", "C": "70 sq cm", "D": "75 sq cm"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Construct triangle with angles in ratio 1:2:3. What type?", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Equilateral"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "Construct ΔPQR with PQ=8cm, PR=10cm, ∠P=60°. What is QR?", "options": {"A": "9cm", "B": "10cm", "C": "11cm", "D": "12cm"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Construct triangle with two sides 5cm, 7cm and non-included angle 30°. How many solutions?", "options": {"A": "0", "B": "1", "C": "2", "D": "Infinite"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "Construct ΔABC with BC=6cm, ∠B=45°, ∠C=75°. What is AB?", "options": {"A": "4.2cm", "B": "5.5cm", "C": "6.8cm", "D": "7.3cm"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "Construct triangle with perimeter 20cm and sides in AP with common difference 2cm. What are sides?", "options": {"A": "4,6,8", "B": "6,8,10", "C": "5,7,9", "D": "7,9,11"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "Construct right triangle with hypotenuse 13cm, one leg 5cm. What is other leg?", "options": {"A": "8cm", "B": "10cm", "C": "12cm", "D": "14cm"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "Construct ΔXYZ with XY=7cm, ∠X=40°, ∠Y=70°. What is XZ?", "options": {"A": "6.5cm", "B": "7.5cm", "C": "8.5cm", "D": "9.5cm"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "Construct triangle with two angles 60° each. What type?", "options": {"A": "Scalene", "B": "Isosceles", "C": "Equilateral", "D": "Right"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "Construct ΔABC with AB=4cm, BC=5cm, CA=6cm. What is ∠B approximately?", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "70°"}, "correct_answer": "D"},
    {"id": 72, "difficulty": "medium", "question": "Construct triangle with base 12cm and two base angles 45° each. What is height?", "options": {"A": "6cm", "B": "8cm", "C": "10cm", "D": "12cm"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Construct ΔPQR with PQ=9cm, QR=12cm, ∠Q=90°. What is PR?", "options": {"A": "13cm", "B": "14cm", "C": "15cm", "D": "16cm"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "Construct triangle with vertices (0,0), (4,0), (0,6). What is perimeter?", "options": {"A": "12 units", "B": "16 units", "C": "18 units", "D": "20 units"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "Construct ΔABC with ∠A=30°, ∠B=90°, BC=5cm. What is AB?", "options": {"A": "5√3 cm", "B": "10cm", "C": "10√3 cm", "D": "15cm"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Construct triangle with sides 8cm, 15cm, 17cm. What is inradius?", "options": {"A": "3cm", "B": "4cm", "C": "5cm", "D": "6cm"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "Construct isosceles triangle with base 16cm, height 15cm. What are equal sides?", "options": {"A": "15cm", "B": "17cm", "C": "19cm", "D": "21cm"}, "correct_answer": "B"},
    {"id": 78, "difficulty": "medium", "question": "Construct ΔXYZ with XY=5cm, YZ=6cm, XZ=7cm. What is longest median?", "options": {"A": "5.5cm", "B": "6.0cm", "C": "6.5cm", "D": "7.0cm"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "Construct triangle with two sides 10cm, 10cm and included angle 120°. What is third side?", "options": {"A": "10√2 cm", "B": "10√3 cm", "C": "20cm", "D": "20√2 cm"}, "correct_answer": "B"},
    {"id": 80, "difficulty": "medium", "question": "Construct ΔABC with AB=6cm, ∠A=45°, ∠C=60°. What is BC approximately?", "options": {"A": "4.9cm", "B": "5.4cm", "C": "5.9cm", "D": "6.4cm"}, "correct_answer": "A"},
    {"id": 81, "difficulty": "hard", "question": "Construct triangle ABC with AB=6cm, BC=7cm, ∠B=135°. What is approximate length of AC?", "options": {"A": "10.8cm", "B": "11.5cm", "C": "12.2cm", "D": "13.4cm"}, "correct_answer": "C"},
    {"id": 82, "difficulty": "hard", "question": "Construct triangle with sides 7cm, 8cm, 9cm. What is area using Heron's formula?", "options": {"A": "12√5 cm²", "B": "12√10 cm²", "C": "24√5 cm²", "D": "24√10 cm²"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Construct ΔPQR with PQ=5cm, QR=6cm, ∠Q=120°. What is approximate area?", "options": {"A": "13.0 cm²", "B": "14.5 cm²", "C": "16.0 cm²", "D": "17.5 cm²"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Construct triangle where two medians are 9cm and 12cm intersecting at right angles. What is third median?", "options": {"A": "10cm", "B": "12cm", "C": "15cm", "D": "18cm"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "Construct ΔABC with AB=8cm, AC=10cm, and median AD=7cm. How many solutions?", "options": {"A": "0", "B": "1", "C": "2", "D": "Infinite"}, "correct_answer": "C"},
       {
      "id": 86,
      "difficulty": "hard",
      "question": "Construct triangle with sides in ratio 3:5:7 and area 150√3 cm². What is perimeter?",
      "options": {"A": "30√10 cm", "B": "45 cm", "C": "50 cm", "D": "60 cm"},
      "correct_answer": "A"
    },    {"id": 87, "difficulty": "hard", "question": "Construct ΔXYZ with XY=6cm, YZ=8cm, and altitude to XZ is 4.8cm. How many triangles possible?", "options": {"A": "0", "B": "1", "C": "2", "D": "Infinite"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "Construct triangle with vertices on circle radius 5cm forming angles 70°, 80°, 30° at center. What type?", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Cannot construct"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "Construct ΔABC with ∠A=60°, ∠B=45°, and circumradius 10cm. What is side AB?", "options": {"A": "10cm", "B": "10√2 cm", "C": "10√3 cm", "D": "20cm"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Construct triangle with sides a,b,c where a²+b²=c²+ab. What is ∠C?", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "C"},
    {"id": 91, "difficulty": "hard", "question": "Construct ΔPQR with PQ=7cm, QR=8cm, and ∠P+∠R=120°. What is PR approximately?", "options": {"A": "9.2cm", "B": "10.1cm", "C": "11.3cm", "D": "12.4cm"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "Construct triangle with two altitudes 6cm and 8cm, and included angle 60°. What is third altitude?", "options": {"A": "4.8cm", "B": "5.2cm", "C": "5.6cm", "D": "6.0cm"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Construct ΔABC with AB=5cm, BC=6cm, and median from B to AC=4cm. What is AC?", "options": {"A": "4cm", "B": "5cm", "C": "6cm", "D": "7cm"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "Construct triangle with sides 5cm, 6cm, 7cm. What is distance between orthocenter and circumcenter?", "options": {"A": "√5 cm", "B": "√6 cm", "C": "√7 cm", "D": "√8 cm"}, "correct_answer": "C"},
    {"id": 95, "difficulty": "hard", "question": "Construct ΔXYZ with XY=8cm, ∠X=75°, ∠Y=60°. What is circumradius?", "options": {"A": "4.0cm", "B": "4.5cm", "C": "5.0cm", "D": "5.5cm"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "Construct triangle with vertices (1,2), (4,6), (8,3). What is centroid?", "options": {"A": "(13/3, 11/3)", "B": "(14/3, 11/3)", "C": "(13/3, 10/3)", "D": "(14/3, 10/3)"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Construct ΔABC with AB=6cm, AC=8cm, and angle bisector of A=5cm. What is BC?", "options": {"A": "7cm", "B": "8cm", "C": "9cm", "D": "10cm"}, "correct_answer": "D"},
    {"id": 98, "difficulty": "hard", "question": "Construct triangle with sides √5 cm, √6 cm, √7 cm. What type?", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Construct ΔPQR with PQ=5cm, QR=7cm, and inradius=1.5cm. What is PR?", "options": {"A": "6cm", "B": "7cm", "C": "8cm", "D": "9cm"}, "correct_answer": "C"},
   {"id": 100, "difficulty": "hard", "question": "Construct triangle with sides 8cm, 15cm, and median to third side=10cm. What is third side?", "options": {"A": "√178 cm", "B": "13 cm", "C": "14 cm", "D": "15 cm"}, "correct_answer": "A"}  ]
}