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X₂₈₆₉¶

ISOGONAL CONJUGATE OF X₂₈₅₅

X₂₈₆₉ is the isogonal conjugate of X₂₈₅₅.

X₂₈₆₉ (ISOGONAL CONJUGATE OF X₂₈₅₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2869 = ISOGONAL CONJUGATE OF X_2855."""

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


        def construct_x_02869(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2869 = ISOGONAL CONJUGATE OF X_2855 on reference triangle ABC."""
            X_2855 = point_from_barycentrics(model, A, B, C, 0.66076696, 1.0042482, -0.66501513, ID="X_2855", classes=["center"])
            X_2869 = isogonal_conjugate(model, A, B, C, X_2855, ID="X_2869", classes=["selected", "target"])
            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_351 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))*(b**(2) + c**(2) - 2*a**(2)))', ID="X_351", classes=["center", "incident"])
            X_878 = point_from_barycentrics(model, A, B, C, -0.14706477, 1.0752646, 0.071800149, ID="X_878", classes=["center", "incident"])
            central_line(model, X_351, X_878, 351, 878, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_2510 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) + c**(2) - a**(2))*(b**(2) - c**(2))*(a**(4) + b**(4) + c**(4) - 3*b**(2)*c**(2)))', ID="X_2510", classes=["center", "incident"])
            central_line(model, X_6, X_2510, 6, 2510, incident=True)
            return promote_point_to_top(model, X_2869)


        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_2869 on the given reference triangle."""
            model = create_model('X_2869 = ISOGONAL CONJUGATE OF X_2855')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02869(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-02869.json"))
            write_center_svg(
                model_acute,
                here / "x-02869.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2869¶

X₂₈₆₉¶