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X₂₃₉₉¶

GIBERT-SIMSON TRANSFORM OF X₁₀₂

X₂₃₉₉ = trilinear pole of line X₁₂₄ X₅₂₂ (the Simson line of X₁₀₂)

X₂₃₉₉ (GIBERT-SIMSON TRANSFORM OF X₁₀₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2399 = GIBERT-SIMSON TRANSFORM OF X_102."""

        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_02399(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2399 = GIBERT-SIMSON TRANSFORM OF X_102 on reference triangle ABC."""
            X_189 = eval_trilinear_point(model, A, B, C, 'b*c/(cos(B) + cos(C) - cos(A) - 1)', ID="X_189", classes=["center"])
            X_514 = eval_trilinear_point(model, A, B, C, '(b - c)/a', ID="X_514", classes=["center"])
            X_102 = eval_trilinear_point(model, A, B, C, '1/(sin(B)*(sec(A) - sec(B)) + sin(C)*(sec(A) - sec(C)))', ID="X_102", classes=["center"])
            X_1311 = eval_barycentric_point(model, A, B, C, '1/(a**(2)*(b**(2) + c**(2)) - a*b*c*(b + c) - (b - c)**(2)*(b**(2) + b*c + c**(2)))', ID="X_1311", classes=["center"])
            central_line(model, X_189, X_514, 189, 514)
            central_line(model, X_102, X_1311, 102, 1311)
            X_2399 = intersect_lines(model, X_189, X_514, X_102, X_1311, ID="X_2399", classes=["selected", "target"])
            X_333 = eval_trilinear_point(model, A, B, C, 'b*c*(b + c - a)/(b + c)', ID="X_333", classes=["center", "incident"])
            X_2432 = point_from_barycentrics(model, A, B, C, -0.48835462, 1.2306536, 0.25770098, ID="X_2432", classes=["center", "incident"])
            central_line(model, X_333, X_2432, 333, 2432, incident=True)
            return promote_point_to_top(model, X_2399)


        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_2399 on the given reference triangle."""
            model = create_model('X_2399 = GIBERT-SIMSON TRANSFORM OF X_102')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02399(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-02399.json"))
            write_center_svg(
                model_acute,
                here / "x-02399.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2399¶

X₂₃₉₉¶