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X₂₃₉₇¶

GIBERT-SIMSON TRANSFORM OF X₁₀₀

X₂₃₉₇ = trilinear pole of line X₁₁₉ X₅₁₇ (the Simson line of X₁₀₀)

X₂₃₉₇ (GIBERT-SIMSON TRANSFORM OF X₁₀₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2397 = GIBERT-SIMSON TRANSFORM OF X_100."""

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


        def construct_x_02397(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2397 = GIBERT-SIMSON TRANSFORM OF X_100 on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center"])
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center"])
            X_644 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(b - c))', ID="X_644", classes=["center"])
            central_line(model, X_2, X_37, 2, 37)
            central_line(model, X_190, X_644, 190, 644)
            X_2397 = intersect_lines(model, X_2, X_37, X_190, X_644, ID="X_2397", classes=["selected", "target"])
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center", "incident"])
            X_1026 = eval_trilinear_point(model, A, B, C, '((b**(2) + c**(2) - a*(b + c))/(b - c))', ID="X_1026", classes=["center", "incident"])
            central_line(model, X_522, X_1026, 522, 1026, incident=True)
            return promote_point_to_top(model, X_2397)


        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_2397 on the given reference triangle."""
            model = create_model('X_2397 = GIBERT-SIMSON TRANSFORM OF X_100')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02397(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-02397.json"))
            write_center_svg(
                model_acute,
                here / "x-02397.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2397¶

X₂₃₉₇¶