56 lines
2.0 KiB
JSON
56 lines
2.0 KiB
JSON
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{
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"coordinate_system": {
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"origin": "B",
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"x_axis_direction": "B→A",
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"unit_scale": "BC=4.5cm → 4.5"
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},
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"elements": {
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"points": [
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{"name": "A", "role": "vertex", "estimated_coord": [3.2, 0]},
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{"name": "B", "role": "vertex", "estimated_coord": [0, 0]},
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{"name": "C", "role": "vertex", "estimated_coord": [0, 4.5]},
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{"name": "G", "role": "centroid", "estimated_coord": [1.6, 1.5]},
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{"name": "P", "role": "orthocenter", "estimated_coord": [1.8, 2.7]},
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{"name": "Q", "role": "circumcenter", "estimated_coord": [1.6, 2.25]},
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{"name": "R", "role": "incenter", "estimated_coord": [1.2, 1.8]}
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],
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"lines": [
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{"type": "segment", "points": ["A", "B"], "properties": ["base_line"]},
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{"type": "segment", "points": ["B", "C"], "properties": ["vertical"]},
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{"type": "segment", "points": ["A", "C"], "properties": ["hypotenuse"]},
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{"type": "ray", "points": ["B", "G"], "direction": "B→G"},
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{"type": "ray", "points": ["A", "P"], "direction": "A→P"}
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],
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"circles": [
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{"center": "Q", "radius_point": "B", "properties": ["dashed"]},
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{"center": "R", "radius_point": "D", "properties": ["solid"]}
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],
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"polygons": [
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{"vertices": ["A","B","C"], "type": "triangle", "properties": ["right_angled_at_B"]}
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]
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},
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"spatial_relations": [
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"AB ⊥ BC (直角符号)",
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"点G ∈ 中线BG",
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"点P ∈ 高线AP",
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"圆Q 外切 △ABC",
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"圆R 内切 △ABC",
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"AG:GD = 2:1 (重心性质)"
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],
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"annotations": {
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"explicit": [
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{"type": "length", "element": "BC", "value": 4.5, "unit": "cm"},
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{"type": "angle", "element": "∠ABC", "value": 90, "unit": "degree"}
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],
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"implicit": [
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"由重心性质得 BG:GG' = 2:1",
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"由垂心性质得 AP⊥BC"
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]
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},
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"confidence_notes": [
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"点D位置未标注→估算为BC中点",
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"圆R半径未标注→基于内切圆公式计算"
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]
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}
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