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X₁₂₂₀¶

ISOGONAL CONJUGATE OF X₁₁₉₃

X₁₂₂₀ is the isogonal conjugate of X₁₁₉₃.

X₁₂₂₀ (ISOGONAL CONJUGATE OF X₁₁₉₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1220 = ISOGONAL CONJUGATE OF X_1193."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            nagel_point_of,
            promote_point_to_top,
            spieker_center_of,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01220(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1220 = ISOGONAL CONJUGATE OF X_1193 on reference triangle ABC."""
            X_1193 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) + c**(2) + a*b + a*c))', ID="X_1193", classes=["center"])
            X_1220 = isogonal_conjugate(model, A, B, C, X_1193, ID="X_1220", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            central_line(model, X_2, X_12, 2, 12, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            central_line(model, X_6, X_8, 6, 8, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_58 = eval_trilinear_point(model, A, B, C, 'a/(b + c)', ID="X_58", classes=["center", "incident"])
            central_line(model, X_10, X_58, 10, 58, incident=True)
            return promote_point_to_top(model, X_1220)


        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_1220 on the given reference triangle."""
            model = create_model('X_1220 = ISOGONAL CONJUGATE OF X_1193')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01220(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-01220.json"))
            write_center_svg(
                model_acute,
                here / "x-01220.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1220¶

X₁₂₂₀¶