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X₂₅₄₃¶

EXSIMILICENTER(BROCARD CIRCLE, (X₄,2R))

The circle (X₄,2R) is identified at X₂₄₇₄.

X₂₅₄₃ (EXSIMILICENTER(BROCARD CIRCLE, (X₄,2R))) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2543 = EXSIMILICENTER(BROCARD CIRCLE, (X_4,2R))."""

        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,
            intersect_lines,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02543(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2543 = EXSIMILICENTER(BROCARD CIRCLE, (X_4,2R)) on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_83 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) + c**(2))', ID="X_83", classes=["center"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_1340 = point_from_barycentrics(model, A, B, C, 0.34709524, 0.36700624, 0.28589852, ID="X_1340", classes=["center"])
            central_line(model, X_4, X_83, 4, 83)
            central_line(model, X_2, X_1340, 2, 1340)
            X_2543 = intersect_lines(model, X_4, X_83, X_2, X_1340, ID="X_2543", classes=["selected", "target"])
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_1341 = point_from_barycentrics(model, A, B, C, 0.30653192, 0.35355532, 0.33991277, ID="X_1341", classes=["center", "incident"])
            central_line(model, X_20, X_1341, 20, 1341, incident=True)
            return promote_point_to_top(model, X_2543)


        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_2543 on the given reference triangle."""
            model = create_model('X_2543 = EXSIMILICENTER(BROCARD CIRCLE, (X_4,2R))')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02543(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-02543.json"))
            write_center_svg(
                model_acute,
                here / "x-02543.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2543¶

X₂₅₄₃¶