{
  "address": "bc73720b7aa68d416956b102f8e908f9",
  "category": "other",
  "question": "What are the circumference and area of a circle with radius 7?",
  "answer": "circumference 43.98, area 153.94",
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  "madeAt": "2026-09-30T22:39:30.722Z",
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    {
      "label": "Circle circumference and area formulas",
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    }
  ],
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  "answerMethod": "method",
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  "source": {
    "kind": "edition_page",
    "value": "Standard geometry reference (e.g. Coxeter, H.S.M. Introduction to Geometry, 2nd ed., Wiley, 1969).",
    "retrieved_utc": "2026-09-30T19:48:00Z"
  },
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    "name": "Circle circumference and area",
    "version": "1",
    "source_url_or_file": "methods/circle-measures.cjs",
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  },
  "method_deck": {
    "inputs": [
      {
        "name": "which_given",
        "type": "string",
        "required": true,
        "description": "Whether value is a radius or a diameter.",
        "enum": [
          "radius",
          "diameter"
        ]
      },
      {
        "name": "value",
        "type": "number",
        "unit": "length units",
        "required": true,
        "description": "The radius or diameter, per which_given.",
        "min": 0
      }
    ],
    "outputs": [
      {
        "name": "circumference",
        "unit": "length units",
        "description": "Circle circumference."
      },
      {
        "name": "area",
        "unit": "square length units",
        "description": "Circle area."
      }
    ],
    "steps": [
      "If which_given is diameter, radius = value / 2; otherwise radius = value.",
      "circumference = 2 * pi * radius.",
      "area = pi * radius^2.",
      "Round both to 2 decimals."
    ],
    "constants": [
      {
        "name": "pi",
        "value": 3.14159265358979,
        "unit": "dimensionless",
        "source": 0
      }
    ],
    "examples": [
      {
        "name": "worked example",
        "inputs": {
          "which_given": "radius",
          "value": 7
        },
        "expected": {
          "answer": "circumference 43.98, area 153.94"
        },
        "check": "By hand: circumference=2*3.14159265*7=43.9823 rounds to 43.98; area=3.14159265*49=153.9380 rounds to 153.94."
      },
      {
        "name": "test vector: given diameter",
        "inputs": {
          "which_given": "diameter",
          "value": 10
        },
        "expected": {
          "answer": "circumference 31.42, area 78.54"
        },
        "check": "By hand: radius=5; circumference=2*3.14159265*5=31.4159 rounds to 31.42; area=3.14159265*25=78.5398 rounds to 78.54; matches the well known fact that a circle of diameter 10 has circumference pi*10=31.4159."
      }
    ],
    "disclaimer": null,
    "deck_category": "geometry"
  },
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  "kind": "method",
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          "value": "Standard geometry reference (e.g. Coxeter, H.S.M. Introduction to Geometry, 2nd ed., Wiley, 1969).",
          "retrieved_utc": "2026-09-30T19:48:00Z"
        },
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        "supersedes": null,
        "added_utc": "2026-09-30T22:39:30.722Z",
        "added_by": "method:Circle circumference and area",
        "why": "the method that computed this answer",
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}