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X₃₅₈¶

2nd MORLEY-TAYLOR-MARR CENTER

X₃₅₈ is the perspector of the adjunct Morley triangle and ABC, and also the Hofstadter 2/3 point.

X₃₅₈ (2nd MORLEY-TAYLOR-MARR CENTER) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_358 = 2nd MORLEY-TAYLOR-MARR CENTER."""

        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,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00358(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_358 = 2nd MORLEY-TAYLOR-MARR CENTER on reference triangle ABC."""
            X_357 = eval_trilinear_point(model, A, B, C, 'sec(A/3)', ID="X_357", classes=["center"])
            X_358 = isogonal_conjugate(model, A, B, C, X_357, ID="X_358", classes=["selected", "target"])
            X_356 = eval_trilinear_point(model, A, B, C, 'cos(A/3) + 2*cos(B/3)*cos(C/3)', ID="X_356", classes=["center", "incident"])
            central_line(model, X_356, X_357, 356, 357, incident=True)
            X_16 = eval_trilinear_point(model, A, B, C, 'sin(A-  pi  /3)', ID="X_16", classes=["center", "incident"])
            X_1135 = eval_trilinear_point(model, A, B, C, 'cos(A/3 + 2*pi  /3)', ID="X_1135", classes=["center", "incident"])
            central_line(model, X_16, X_1135, 16, 1135, incident=True)
            return promote_point_to_top(model, X_358)


        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_358 on the given reference triangle."""
            model = create_model('X_358 = 2nd MORLEY-TAYLOR-MARR CENTER')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00358(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-00358.json"))
            write_center_svg(
                model_acute,
                here / "x-00358.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X358¶

X₃₅₈¶