← etc / Encyclopedia of Triangle Centers

X₂₄₀₈¶

GIBERT-SIMSON TRANSFORM OF X₁₁₁

X₂₄₀₈ (GIBERT-SIMSON TRANSFORM OF X₁₁₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2408 = GIBERT-SIMSON TRANSFORM OF X_111."""

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


        def construct_x_02408(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2408 = GIBERT-SIMSON TRANSFORM OF X_111 on reference triangle ABC."""
            X_2408 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(2) - c**(2))*(5*a**(2) - b**(2) - c**(2))/(2*a**(2) - b**(2) - c**(2)))', ID="X_2408", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", 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_2, X_523, 2, 523, incident=True)
            X_690 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))*(2*a**(2) - b**(2) - c**(2))', ID="X_690", classes=["center", "incident"])
            X_895 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2) - a**(2))/(b**(2) + c**(2) - 2*a**(2))', ID="X_895", classes=["center", "incident"])
            central_line(model, X_690, X_895, 690, 895, incident=True)
            X_691 = eval_trilinear_point(model, A, B, C, 'a/((b**(2) - c**(2))*(2*a**(2) - b**(2) - c**(2)))', ID="X_691", classes=["center", "incident"])
            X_2407 = eval_trilinear_point(model, A, B, C, '(csc(C - A)*cos(C) - csc(A - B)*cos(B))*(csc(B - C)/a)**(2)', ID="X_2407", classes=["center", "incident"])
            central_line(model, X_691, X_2407, 691, 2407, incident=True)
            return promote_point_to_top(model, X_2408)


        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_2408 on the given reference triangle."""
            model = create_model('X_2408 = GIBERT-SIMSON TRANSFORM OF X_111')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02408(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-02408.json"))
            write_center_svg(
                model_acute,
                here / "x-02408.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2408¶

X₂₄₀₈¶