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X₂₈₀₅¶

ISOGONAL CONJUGATE OF X₂₇₂₁

X₂₈₀₅ is the isogonal conjugate of X₂₇₂₁.

X₂₈₀₅ (ISOGONAL CONJUGATE OF X₂₇₂₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2805 = ISOGONAL CONJUGATE OF X_2721."""

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


        def construct_x_02805(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2805 = ISOGONAL CONJUGATE OF X_2721 on reference triangle ABC."""
            X_2721 = point_from_barycentrics(model, A, B, C, 0.60995165, -0.33022499, 0.72027334, ID="X_2721", classes=["center"])
            X_2805 = isogonal_conjugate(model, A, B, C, X_2721, ID="X_2805", classes=["selected", "target"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_126 = eval_trilinear_point(model, A, B, C, '(b*c*(2*a**(2) - b**(2) - c**(2))*(b**(4) + c**(4) + a**(2)*(b**(2) + c**(2)) - 4*b**(2)*c**(2)))', ID="X_126", classes=["center", "incident"])
            central_line(model, X_11, X_126, 11, 126, incident=True)
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            central_line(model, X_37, X_100, 37, 100, incident=True)
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            X_149 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(3) + c**(3) - a**(3) + (a**(2) - b*c)*(b + c) + a*(b*c - b**(2) - c**(2))))', ID="X_149", classes=["center", "incident"])
            central_line(model, X_75, X_149, 75, 149, incident=True)
            return promote_point_to_top(model, X_2805)


        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_2805 on the given reference triangle."""
            model = create_model('X_2805 = ISOGONAL CONJUGATE OF X_2721')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02805(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-02805.json"))
            write_center_svg(
                model_acute,
                here / "x-02805.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2805¶

X₂₈₀₅¶