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