← etc / Encyclopedia of Triangle Centers

X₂₄₆₃¶

INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE)

X₂₄₆₃ is the insimilicenter(orthocentroidal circle, incircle).

X₂₄₆₃ (INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2463 = INSIMILICENTER(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,
            nagel_point_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02463(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2463 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) on reference triangle ABC."""
            X_2463 = eval_trilinear_point(model, A, B, C, '(J + cos(A) + 4*cos(B)*cos(C))', ID="X_2463", 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_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_2468 = eval_trilinear_point(model, A, B, C, '(b*c*(a*cos(A) + 4*a*cos(B)*cos(C) - (b + c)*J))', ID="X_2468", classes=["center", "incident"])
            central_line(model, X_2, X_2468, 2, 2468, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", 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_8, X_2467, 8, 2467, incident=True)
            return promote_point_to_top(model, X_2463)


        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_2463 on the given reference triangle."""
            model = create_model('X_2463 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02463(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-02463.json"))
            write_center_svg(
                model_acute,
                here / "x-02463.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2463¶

X₂₄₆₃¶