← etc / Encyclopedia of Triangle Centers

X₂₄₁₃¶

GIBERT-SIMSON TRANSFORM OF X₁₁₄₁

X₂₄₁₃ = trilinear pole of line X₁₃₇ X₁₅₁₀ (the Simson line of X₁₁₄₁)

X₂₄₁₃ (GIBERT-SIMSON TRANSFORM OF X₁₁₄₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2413 = GIBERT-SIMSON TRANSFORM OF X_1141."""

        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,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02413(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2413 = GIBERT-SIMSON TRANSFORM OF X_1141 on reference triangle ABC."""
            X_2413 = point_from_barycentrics(model, A, B, C, -0.049419878, 0.94479088, 0.104629, ID="X_2413", classes=["selected", "target"])
            return promote_point_to_top(model, X_2413)


        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_2413 on the given reference triangle."""
            model = create_model('X_2413 = GIBERT-SIMSON TRANSFORM OF X_1141')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02413(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-02413.json"))
            write_center_svg(
                model_acute,
                here / "x-02413.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2413¶

X₂₄₁₃¶