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X₂₈₀₇¶

ISOGONAL CONJUGATE OF X₂₇₂₃

X₂₈₀₇ is the isogonal conjugate of X₂₇₂₃.

X₂₈₀₇ (ISOGONAL CONJUGATE OF X₂₇₂₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2807 = ISOGONAL CONJUGATE OF X_2723."""

        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,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02807(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2807 = ISOGONAL CONJUGATE OF X_2723 on reference triangle ABC."""
            X_2723 = point_from_barycentrics(model, A, B, C, 1.0392316, 0.18668831, -0.22591991, ID="X_2723", classes=["center"])
            X_2807 = isogonal_conjugate(model, A, B, C, X_2723, ID="X_2807", classes=["selected", "target"])
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", 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_55, X_103, 55, 103, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_185 = eval_trilinear_point(model, A, B, C, '(cos(A))*(1 - cos(A)*cos(B - C))', ID="X_185", classes=["center", "incident"])
            central_line(model, X_1, X_185, 1, 185, incident=True)
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            X_102 = eval_trilinear_point(model, A, B, C, '1/(sin(B)*(sec(A) - sec(B)) + sin(C)*(sec(A) - sec(C)))', ID="X_102", classes=["center", "incident"])
            central_line(model, X_101, X_102, 101, 102, incident=True)
            return promote_point_to_top(model, X_2807)


        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_2807 on the given reference triangle."""
            model = create_model('X_2807 = ISOGONAL CONJUGATE OF X_2723')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02807(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-02807.json"))
            write_center_svg(
                model_acute,
                here / "x-02807.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2807¶

X₂₈₀₇¶