[
  {
    "id": "template-001",
    "topic": "Triangle Angle Sum",
    "difficulty": "easy",
    "stem": "A triangle has angles measuring 50° and 60°. What is the measure of the third angle?",
    "choices": ["50°", "60°", "70°", "80°"],
    "correctIndex": 2,
    "explanations": [
      "50° would make the three angles sum to 160°, not 180° — every triangle's interior angles sum to exactly 180°.",
      "60° would repeat the second given angle and sum to 170°, not 180°.",
      "Correct — 180° minus (50° + 60°) leaves 70° for the third angle, which is the defining property of a triangle's interior angle sum.",
      "80° overshoots: 50° + 60° + 80° = 190°, more than a triangle's angles can ever sum to."
    ],
    "hint": "The three interior angles of any triangle always add up to the same fixed total. Subtract the two known angles from that total."
  },
  {
    "id": "template-002",
    "topic": "Triangle Angle Sum",
    "difficulty": "medium",
    "stem": "In triangle ABC, angle A is twice angle B, and angle C is 30°. What is the measure of angle B?",
    "choices": ["30°", "40°", "50°", "60°"],
    "correctIndex": 2,
    "explanations": [
      "30° would make angle A = 60°, and 30° + 60° + 30° = 120°, short of the required 180°.",
      "40° would make angle A = 80°, and 40° + 80° + 30° = 150°, still short of 180°.",
      "Correct — with angle B = x and angle A = 2x, x + 2x + 30° = 180° gives 3x = 150°, so x = 50°.",
      "60° would make angle A = 120°, and 60° + 120° + 30° = 210°, more than a triangle allows."
    ],
    "hint": "Let angle B = x. Angle A is 2x. Write one equation using the fact that all three angles sum to 180°, then solve for x."
  },
  {
    "id": "template-003",
    "topic": "Circle Theorems",
    "difficulty": "hard",
    "stem": "A chord is 8 units from the center of a circle with radius 10 units. What is the length of the chord?",
    "choices": ["6 units", "12 units", "16 units", "18 units"],
    "correctIndex": 2,
    "explanations": [
      "6 units is the length of the half-chord, not the full chord — it still needs to be doubled.",
      "12 units doesn't match the right triangle formed by the radius, the distance to the center, and the half-chord.",
      "Correct — the radius, the perpendicular distance to the center, and half the chord form a right triangle: half-chord = √(10² − 8²) = 6, so the full chord is 2 × 6 = 16.",
      "18 units overstates the chord; check the right-triangle relationship again."
    ],
    "hint": "A line from the center perpendicular to a chord bisects it. That perpendicular distance, the radius, and half the chord form a right triangle — the Pythagorean theorem applies.",
    "diagram": "",
    "diagramCaption": ""
  }
]