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X₂₄₁₉¶

GIBERT-SIMSON TRANSFORM OF X₁₂₉₇

X₂₄₁₉ = trilinear pole of line X₁₂₇ X₅₂₅ (the Simson line of X₁₂₉₇)

X₂₄₁₉ (GIBERT-SIMSON TRANSFORM OF X₁₂₉₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2419 = GIBERT-SIMSON TRANSFORM OF X_1297."""

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


        def construct_x_02419(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2419 = GIBERT-SIMSON TRANSFORM OF X_1297 on reference triangle ABC."""
            X_253 = eval_trilinear_point(model, A, B, C, '((csc(A))/(tan(B) + tan(C) - tan(A)))', ID="X_253", classes=["center"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", 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"])
            X_2373 = point_from_barycentrics(model, A, B, C, 0.69246829, 0.98040184, -0.67287013, ID="X_2373", classes=["center"])
            central_line(model, X_253, X_523, 253, 523)
            central_line(model, X_1297, X_2373, 1297, 2373)
            X_2419 = intersect_lines(model, X_253, X_523, X_1297, X_2373, ID="X_2419", classes=["selected", "target"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_2435 = point_from_barycentrics(model, A, B, C, -2.0119632, 2.7150562, 0.29690708, ID="X_2435", classes=["center", "incident"])
            central_line(model, X_69, X_2435, 69, 2435, incident=True)
            return promote_point_to_top(model, X_2419)


        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_2419 on the given reference triangle."""
            model = create_model('X_2419 = GIBERT-SIMSON TRANSFORM OF X_1297')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02419(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-02419.json"))
            write_center_svg(
                model_acute,
                here / "x-02419.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2419¶

X₂₄₁₉¶