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X₂₄₃₅¶

ISOGONAL CONJUGATE OF X₂₄₀₉

X₂₄₃₅ is the isogonal conjugate of X₂₄₀₉.

X₂₄₃₅ (ISOGONAL CONJUGATE OF X₂₄₀₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2435 = ISOGONAL CONJUGATE OF X_2409."""

        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,
            isogonal_conjugate,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02435(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2435 = ISOGONAL CONJUGATE OF X_2409 on reference triangle ABC."""
            X_2409 = point_from_barycentrics(model, A, B, C, -0.074912795, 0.079939185, 0.99497361, ID="X_2409", classes=["center"])
            X_2435 = isogonal_conjugate(model, A, B, C, X_2409, ID="X_2435", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_520 = eval_trilinear_point(model, A, B, C, '(cos(A))*(sin(2*B) - sin(2*C))', ID="X_520", classes=["center", "incident"])
            central_line(model, X_6, X_520, 6, 520, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_525 = eval_trilinear_point(model, A, B, C, '(b*cos(B) - c*cos(C))/a', ID="X_525", classes=["center", "incident"])
            central_line(model, X_4, X_525, 4, 525, incident=True)
            X_64 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - cos(B)*cos(C))', ID="X_64", classes=["center", "incident"])
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            central_line(model, X_64, X_512, 64, 512, incident=True)
            return promote_point_to_top(model, X_2435)


        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_2435 on the given reference triangle."""
            model = create_model('X_2435 = ISOGONAL CONJUGATE OF X_2409')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02435(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-02435.json"))
            write_center_svg(
                model_acute,
                here / "x-02435.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2435¶

X₂₄₃₅¶