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X₂₄₆₄¶

EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE)

X₂₄₆₄ is the exsimilicenter(orthocentroidal circle, incircle).

X₂₄₆₄ (EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2464 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE)."""

        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,
            incenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02464(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2464 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) on reference triangle ABC."""
            X_2464 = eval_trilinear_point(model, A, B, C, '(J - cos(A) - 4*cos(B)*cos(C))', ID="X_2464", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_381 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) - cos(A)', ID="X_381", classes=["center", "incident"])
            central_line(model, X_1, X_381, 1, 381, incident=True)
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_1345 = eval_trilinear_point(model, A, B, C, '( OH  - R)*cos(A) - 4*R*cos(B)*cos(C)', ID="X_1345", classes=["center", "incident"])
            central_line(model, X_56, X_1345, 56, 1345, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_2467 = point_from_barycentrics(model, A, B, C, 0.29344052, 0.3004125, 0.40614698, ID="X_2467", classes=["center", "incident"])
            central_line(model, X_2, X_2467, 2, 2467, incident=True)
            return promote_point_to_top(model, X_2464)


        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_2464 on the given reference triangle."""
            model = create_model('X_2464 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02464(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-02464.json"))
            write_center_svg(
                model_acute,
                here / "x-02464.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2464¶

X₂₄₆₄¶