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X₂₈₇₁¶

ISOGONAL CONJUGATE OF X₂₈₅₇

X₂₈₇₁ is the isogonal conjugate of X₂₈₅₇.

X₂₈₇₁ (ISOGONAL CONJUGATE OF X₂₈₅₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2871 = ISOGONAL CONJUGATE OF X_2857."""

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


        def construct_x_02871(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2871 = ISOGONAL CONJUGATE OF X_2857 on reference triangle ABC."""
            X_2857 = eval_barycentric_point(model, A, B, C, '(a**(6)*(b**(2) + c**(2)) - 2*a**(4)*(b**(4) + c**(4)) + a**(2)*(b**(6) + c**(6)) + b**(2)*c**(2)*(b**(2) - c**(2))**(2)) / (a**(6)*(b**(2) + c**(2)) - a**(4)*(b**(2) + c**(2))**(2) + a**(2)*(b**(6) + c**(6)) - (b**(2) - c**(2))**(2)*(b**(2) - b*c + c**(2))*(b**(2) + b*c + c**(2)))', ID="X_2857", classes=["center"])
            X_2871 = isogonal_conjugate(model, A, B, C, X_2857, ID="X_2871", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_157 = eval_trilinear_point(model, A, B, C, '(a*(b**(3)*cos(B) + c**(3)*cos(C) - a**(3)*cos(A)))', ID="X_157", classes=["center", "incident"])
            central_line(model, X_6, X_157, 6, 157, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            X_53 = eval_trilinear_point(model, A, B, C, 'tan(A)*cos(B - C)', ID="X_53", classes=["center", "incident"])
            X_1843 = eval_trilinear_point(model, A, B, C, 'tan(A)*sin(A +  omega  )', ID="X_1843", classes=["center", "incident"])
            central_line(model, X_53, X_1843, 53, 1843, incident=True)
            return promote_point_to_top(model, X_2871)


        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_2871 on the given reference triangle."""
            model = create_model('X_2871 = ISOGONAL CONJUGATE OF X_2857')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02871(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-02871.json"))
            write_center_svg(
                model_acute,
                here / "x-02871.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2871¶

X₂₈₇₁¶