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X₂₄₆₅¶

INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE)

X₂₄₆₅ is the insimilicenter(orthocentroidal circle, 2nd Lemoine circle).

X₂₄₆₅ (INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2465 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE)."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02465(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2465 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE) on reference triangle ABC."""
            X_2465 = eval_trilinear_point(model, A, B, C, '(cos(A) + 4*cos(B)*cos(C) + J*sin(A))', ID="X_2465", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_13 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /3)', ID="X_13", classes=["center", "incident"])
            central_line(model, X_6, X_13, 6, 13, incident=True)
            X_1124 = eval_trilinear_point(model, A, B, C, '1 + sin(A)', ID="X_1124", classes=["center", "incident"])
            X_2464 = eval_trilinear_point(model, A, B, C, '(J - cos(A) - 4*cos(B)*cos(C))', ID="X_2464", classes=["center", "incident"])
            central_line(model, X_1124, X_2464, 1124, 2464, incident=True)
            X_1335 = eval_trilinear_point(model, A, B, C, '(1 - sin(A))', ID="X_1335", classes=["center", "incident"])
            X_2463 = eval_trilinear_point(model, A, B, C, '(J + cos(A) + 4*cos(B)*cos(C))', ID="X_2463", classes=["center", "incident"])
            central_line(model, X_1335, X_2463, 1335, 2463, incident=True)
            return promote_point_to_top(model, X_2465)


        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_2465 on the given reference triangle."""
            model = create_model('X_2465 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02465(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-02465.json"))
            write_center_svg(
                model_acute,
                here / "x-02465.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2465¶

X₂₄₆₅¶