← etc / Encyclopedia of Triangle Centers

X₆₄₀¶

COMPLEMENT OF X₃₇₂

X₆₄₀ (COMPLEMENT OF X₃₇₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_640 = COMPLEMENT OF X_372."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nine_point_center_of,
            point_from_barycentrics,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00640(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_640 = COMPLEMENT OF X_372 on reference triangle ABC."""
            X_639 = point_from_barycentrics(model, A, B, C, 0.35035787, 0.32442401, 0.32521812, ID="X_639", classes=["center"])
            X_626 = eval_trilinear_point(model, A, B, C, '(b**(4) + c**(4))/a', ID="X_626", classes=["center"])
            X_640 = reflection_in_point(model, X_639, X_626, ID="X_640", classes=["selected", "target"], guide=False)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center", "incident"])
            central_line(model, X_5, X_141, 5, 141, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_372 = eval_trilinear_point(model, A, B, C, 'cos(A +  pi  /4)', ID="X_372", classes=["center", "incident"])
            central_line(model, X_2, X_372, 2, 372, incident=True)
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_486 = eval_trilinear_point(model, A, B, C, 'sec(A +  pi  /4)', ID="X_486", classes=["center", "incident"])
            central_line(model, X_69, X_486, 69, 486, incident=True)
            return promote_point_to_top(model, X_640)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_640 on the given reference triangle."""
            model = create_model('X_640 = COMPLEMENT OF X_372')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00640(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-00640.json"))
            write_center_svg(
                model_acute,
                here / "x-00640.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X640¶

X₆₄₀¶