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X₂₈₀₉¶

ISOGONAL CONJUGATE OF X₂₇₂₅

X₂₈₀₉ is the isogonal conjugate of X₂₇₂₅.

X₂₈₀₉ (ISOGONAL CONJUGATE OF X₂₇₂₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2809 = ISOGONAL CONJUGATE OF X_2725."""

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


        def construct_x_02809(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2809 = ISOGONAL CONJUGATE OF X_2725 on reference triangle ABC."""
            X_2725 = point_from_barycentrics(model, A, B, C, 0.76388889, -0.28333333, 0.51944444, ID="X_2725", classes=["center"])
            X_2809 = isogonal_conjugate(model, A, B, C, X_2725, ID="X_2809", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center", "incident"])
            central_line(model, X_1, X_41, 1, 41, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_116 = eval_trilinear_point(model, A, B, C, 'b*c*((b - c)**(2)*(b**(2) + b*c + c**(2) - a*b - a*c))', ID="X_116", classes=["center", "incident"])
            central_line(model, X_10, X_116, 10, 116, incident=True)
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_103 = eval_trilinear_point(model, A, B, C, 'a/((a - b)*cot(C) + (a - c)*cot(B))', ID="X_103", classes=["center", "incident"])
            central_line(model, X_40, X_103, 40, 103, incident=True)
            return promote_point_to_top(model, X_2809)


        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_2809 on the given reference triangle."""
            model = create_model('X_2809 = ISOGONAL CONJUGATE OF X_2725')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02809(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-02809.json"))
            write_center_svg(
                model_acute,
                here / "x-02809.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2809¶

X₂₈₀₉¶