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X₃₄₃₂¶

X₅-VERTEX CONJUGATE OF X₅

X₃₄₃₂ (X₅-VERTEX CONJUGATE OF X₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3432 = X_5-VERTEX CONJUGATE OF X_5."""

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


        def construct_x_03432(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3432 = X_5-VERTEX CONJUGATE OF X_5 on reference triangle ABC."""
            X_2888 = eval_barycentric_point(model, A, B, C, 'a**(10) - 3*a**(8)*(b**(2) + c**(2)) + a**(6)*(4*b**(4) + 5*b**(2)*c**(2) + 4*c**(4)) - 2*a**(4)*(2*b**(6) + b**(4)*c**(2) + b**(2)*c**(4) + 2*c**(6)) + 3*a**(2)*(b**(8) - b**(6)*c**(2) - b**(2)*c**(6) + c**(8)) - (b**(2) - c**(2))**(4)*(b**(2) + c**(2))', ID="X_2888", classes=["center"])
            X_3432 = isogonal_conjugate(model, A, B, C, X_2888, ID="X_3432", classes=["selected", "target"])
            X_49 = eval_trilinear_point(model, A, B, C, 'cos(3*A)', ID="X_49", classes=["center", "incident"])
            X_52 = eval_trilinear_point(model, A, B, C, 'cos(2*A)*cos(B - C)', ID="X_52", classes=["center", "incident"])
            central_line(model, X_49, X_52, 49, 52, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_1601 = point_from_barycentrics(model, A, B, C, 0.43272298, 0.23120612, 0.3360709, ID="X_1601", classes=["center", "incident"])
            central_line(model, X_5, X_1601, 5, 1601, incident=True)
            return promote_point_to_top(model, X_3432)


        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_3432 on the given reference triangle."""
            model = create_model('X_3432 = X_5-VERTEX CONJUGATE OF X_5')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03432(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-03432.json"))
            write_center_svg(
                model_acute,
                here / "x-03432.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3432¶

X₃₄₃₂¶