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X₃₂₇₂¶

CENTER OF EQUILATERAL TRIANGLE J1J2J3

Let A₁B₁C₁, A₂B₂C₂, A₃B₃C₃ be the 1st Morley, 2nd Morley and 3rd Morley triangles of ABC, respectively. Then {A, A₁, A₂, A₃} are concyclic on a circle, A0.

X₃₂₇₂ (CENTER OF EQUILATERAL TRIANGLE J1J2J3) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3272 = CENTER OF EQUILATERAL TRIANGLE J1J2J3."""

        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,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03272(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3272 = CENTER OF EQUILATERAL TRIANGLE J1J2J3 on reference triangle ABC."""
            X_3272 = eval_trilinear_point(model, A, B, C, 'cos(B/3 - C/3)', ID="X_3272", classes=["selected", "target"])
            X_396 = eval_trilinear_point(model, A, B, C, 'cos(B - C) + 2*cos(A -  pi  /3)', ID="X_396", classes=["center", "incident"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            central_line(model, X_396, X_523, 396, 523, incident=True)
            X_357 = eval_trilinear_point(model, A, B, C, 'sec(A/3)', ID="X_357", 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_357, X_1135, 357, 1135, incident=True)
            X_358 = eval_trilinear_point(model, A, B, C, 'cos(A/3)', ID="X_358", classes=["center", "incident"])
            X_1136 = eval_trilinear_point(model, A, B, C, '1/cos(A/3 + 4*pi  /3)', ID="X_1136", classes=["center", "incident"])
            central_line(model, X_358, X_1136, 358, 1136, incident=True)
            return promote_point_to_top(model, X_3272)


        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_3272 on the given reference triangle."""
            model = create_model('X_3272 = CENTER OF EQUILATERAL TRIANGLE J1J2J3')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03272(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-03272.json"))
            write_center_svg(
                model_acute,
                here / "x-03272.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3272¶

X₃₂₇₂¶