← etc / Encyclopedia of Triangle Centers

X₃₅₆¶

MORLEY CENTER

X₃₅₆ is the centroid of the Morley equilateral triangle. For a discussion of the theorem and extensive list of references, see

X₃₅₆ (MORLEY CENTER) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_356 = MORLEY 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00356(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_356 = MORLEY CENTER on reference triangle ABC."""
            X_356 = eval_trilinear_point(model, A, B, C, 'cos(A/3) + 2*cos(B/3)*cos(C/3)', ID="X_356", classes=["selected", "target"])
            X_357 = eval_trilinear_point(model, A, B, C, 'sec(A/3)', ID="X_357", classes=["center", "incident"])
            X_358 = eval_trilinear_point(model, A, B, C, 'cos(A/3)', ID="X_358", classes=["center", "incident"])
            central_line(model, X_357, X_358, 357, 358, incident=True)
            X_1134 = eval_trilinear_point(model, A, B, C, '1/cos(A/3 + 2*pi  /3)', ID="X_1134", 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_1134, X_1135, 1134, 1135, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_3278 = eval_trilinear_point(model, A, B, C, '(cos(A/3)*cos(2*A/3) + cos(B/3)*cos(C/3))', ID="X_3278", classes=["center", "incident"])
            central_line(model, X_3, X_3278, 3, 3278, incident=True)
            return promote_point_to_top(model, X_356)


        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_356 on the given reference triangle."""
            model = create_model('X_356 = MORLEY CENTER')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00356(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-00356.json"))
            write_center_svg(
                model_acute,
                here / "x-00356.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X356¶

X₃₅₆¶