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X₂₁₃₈¶

EIGENTRANSFORM OF X₆₉

X₂₁₃₈ (EIGENTRANSFORM OF X₆₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2138 = EIGENTRANSFORM OF X_69."""

        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,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02138(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2138 = EIGENTRANSFORM OF X_69 on reference triangle ABC."""
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_64 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - cos(B)*cos(C))', ID="X_64", classes=["center"])
            X_1249 = eval_trilinear_point(model, A, B, C, '(tan(A))*(cos(A) - cos(B)*cos(C))', ID="X_1249", classes=["center"])
            X_1941 = eval_trilinear_point(model, A, B, C, '(cos(B)*cos(C)*((cos(A))**(4) + (cos(B))**(2)*(cos(C))**(2)))', ID="X_1941", classes=["center"])
            central_line(model, X_6, X_64, 6, 64)
            central_line(model, X_1249, X_1941, 1249, 1941)
            X_2138 = intersect_lines(model, X_6, X_64, X_1249, X_1941, ID="X_2138", classes=["selected", "target"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_2139 = point_from_barycentrics(model, A, B, C, 0.67949204, 0.47837797, -0.15787001, ID="X_2139", classes=["center", "incident"])
            central_line(model, X_69, X_2139, 69, 2139, incident=True)
            return promote_point_to_top(model, X_2138)


        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_2138 on the given reference triangle."""
            model = create_model('X_2138 = EIGENTRANSFORM OF X_69')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02138(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-02138.json"))
            write_center_svg(
                model_acute,
                here / "x-02138.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2138¶

X₂₁₃₈¶