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X₁₁₃₃¶

BURGESS POINT

Rotate line BC about B away from A through angle B/3, and rotate line BC about C away from A through angle C/3; let A' be the point in which the two rotated lines meet. Define B' and C' cyclically. Let A″ be the point of intersection of lines BC' and B'C, and define B″ and C″ cyclically. The lines AA', BB', CC' concur in X₃₅₇, and AA″, BB″, CC″ concur in X₃₅₈. The first of these with reference to triangle A'B'C' is X₁₁₃₃; i.e., X₁₁₃₃ = X₃₅₇-of-A'B'C'.

X₁₁₃₃ (BURGESS POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1133 = BURGESS POINT."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

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


        def construct_x_01133(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1133 = BURGESS POINT on reference triangle ABC."""
            X_1133 = eval_trilinear_point(model, A, B, C, 'sin( pi  /3 - A/3)/sin( pi  /3 + A/3)', ID="X_1133", classes=["selected", "target"])
            return promote_point_to_top(model, X_1133)


        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_1133 on the given reference triangle."""
            model = create_model('X_1133 = BURGESS POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01133(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-01133.json"))
            write_center_svg(
                model_acute,
                here / "x-01133.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1133¶

X₁₁₃₃¶