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X₂₄₁₆¶

GIBERT-SIMSON TRANSFORM OF X₁₂₉₄

X₂₄₁₆ = trilinear pole of line X₁₂₂ X₅₂₀ (the Simson line of X₁₂₉₄)

X₂₄₁₆ (GIBERT-SIMSON TRANSFORM OF X₁₂₉₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2416 = GIBERT-SIMSON TRANSFORM OF X_1294."""

        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_barycentric_point,
            eval_trilinear_point,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02416(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2416 = GIBERT-SIMSON TRANSFORM OF X_1294 on reference triangle ABC."""
            X_525 = eval_trilinear_point(model, A, B, C, '(b*cos(B) - c*cos(C))/a', ID="X_525", classes=["center"])
            X_1073 = eval_trilinear_point(model, A, B, C, '((cot(A))/(cos(A) - cos(B)*cos(C)))', ID="X_1073", classes=["center"])
            X_1294 = eval_barycentric_point(model, A, B, C, '1/(a**(6)*(b**(2) + c**(2)) - a**(4)*(3*b**(4) - 4*b**(2)*c**(2) + 3*c**(4)) + 3*a**(2)*(b**(2) - c**(2))**(2)*(b**(2) + c**(2)) - (b**(2) - c**(2))**(2)*(b**(4) + 4*b**(2)*c**(2) + c**(4)))', ID="X_1294", classes=["center"])
            X_1297 = eval_trilinear_point(model, A, B, C, '(a/(b**(6) + c**(6) - 2*a**(6) + a**(4)*b**(2) + a**(4)*c**(2) - b**(4)*c**(2) - b**(2)*c**(4)))', ID="X_1297", classes=["center"])
            central_line(model, X_525, X_1073, 525, 1073)
            central_line(model, X_1294, X_1297, 1294, 1297)
            X_2416 = intersect_lines(model, X_525, X_1073, X_1294, X_1297, ID="X_2416", classes=["selected", "target"])
            X_394 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A)', ID="X_394", classes=["center", "incident"])
            X_2430 = point_from_barycentrics(model, A, B, C, -7.9968774, 8.569498, 0.42737949, ID="X_2430", classes=["center", "incident"])
            central_line(model, X_394, X_2430, 394, 2430, incident=True)
            return promote_point_to_top(model, X_2416)


        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_2416 on the given reference triangle."""
            model = create_model('X_2416 = GIBERT-SIMSON TRANSFORM OF X_1294')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02416(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-02416.json"))
            write_center_svg(
                model_acute,
                here / "x-02416.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2416¶

X₂₄₁₆¶