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X₂₇₉₆¶

ISOGONAL CONJUGATE OF X₂₇₁₂

X₂₇₉₆ is the isogonal conjugate of X₂₇₁₂.

X₂₇₉₆ (ISOGONAL CONJUGATE OF X₂₇₁₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2796 = ISOGONAL CONJUGATE OF X_2712."""

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


        def construct_x_02796(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2796 = ISOGONAL CONJUGATE OF X_2712 on reference triangle ABC."""
            X_2712 = point_from_barycentrics(model, A, B, C, 0.50038468, -0.33025401, 0.82986933, ID="X_2712", classes=["center"])
            X_2796 = isogonal_conjugate(model, A, B, C, X_2712, ID="X_2796", classes=["selected", "target"])
            X_86 = eval_trilinear_point(model, A, B, C, 'b*c/(b + c)', ID="X_86", classes=["center", "incident"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            central_line(model, X_86, X_99, 86, 99, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            central_line(model, X_10, X_190, 10, 190, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_121 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c - 2*a)*(b**(3) + c**(3) + a*(b**(2) + c**(2)) - 2*b*c*(b + c)))', ID="X_121", classes=["center", "incident"])
            central_line(model, X_115, X_121, 115, 121, incident=True)
            return promote_point_to_top(model, X_2796)


        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_2796 on the given reference triangle."""
            model = create_model('X_2796 = ISOGONAL CONJUGATE OF X_2712')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02796(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-02796.json"))
            write_center_svg(
                model_acute,
                here / "x-02796.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2796¶

X₂₇₉₆¶