← etc / Encyclopedia of Triangle Centers

X₃₂₇₆¶

CENTER OF 2nd MORLEY TRIANGLE

X₃₂₇₆ (CENTER OF 2nd MORLEY TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3276 = CENTER OF 2nd MORLEY TRIANGLE."""

        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_03276(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3276 = CENTER OF 2nd MORLEY TRIANGLE on reference triangle ABC."""
            X_3276 = eval_trilinear_point(model, A, B, C, 'cos(A/3 - 2*pi  /3) + 2*cos(B/3 - 2*pi  /3)*cos(C/3 - 2*pi  /3)', ID="X_3276", 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"])
            X_357 = eval_trilinear_point(model, A, B, C, 'sec(A/3)', ID="X_357", classes=["center", "incident"])
            central_line(model, X_356, X_357, 356, 357, incident=True)
            X_1136 = eval_trilinear_point(model, A, B, C, '1/cos(A/3 + 4*pi  /3)', ID="X_1136", classes=["center", "incident"])
            X_1137 = eval_trilinear_point(model, A, B, C, '(cos(A/3 + 4*pi  /3))', ID="X_1137", classes=["center", "incident"])
            central_line(model, X_1136, X_1137, 1136, 1137, incident=True)
            X_3272 = eval_trilinear_point(model, A, B, C, 'cos(B/3 - C/3)', ID="X_3272", classes=["center", "incident"])
            X_3274 = eval_trilinear_point(model, A, B, C, 'cos(A/3 +  pi  /6)', ID="X_3274", classes=["center", "incident"])
            central_line(model, X_3272, X_3274, 3272, 3274, incident=True)
            return promote_point_to_top(model, X_3276)


        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_3276 on the given reference triangle."""
            model = create_model('X_3276 = CENTER OF 2nd MORLEY TRIANGLE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03276(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-03276.json"))
            write_center_svg(
                model_acute,
                here / "x-03276.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3276¶

X₃₂₇₆¶