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X₃₁₁₇¶

ISOGONAL CONJUGATE OF TgX(32)

X₃₁₁₇ is the isogonal conjugate of tgx(32).

X₃₁₁₇ (ISOGONAL CONJUGATE OF TgX(32)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3117 = ISOGONAL CONJUGATE OF TgX(32)."""

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


        def construct_x_03117(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3117 = ISOGONAL CONJUGATE OF TgX(32) on reference triangle ABC."""
            X_3114 = eval_trilinear_point(model, A, B, C, '1/(a**(3)*(b**(4) + c**(4) + b**(2)*c**(2)))', ID="X_3114", classes=["center"])
            X_3117 = isogonal_conjugate(model, A, B, C, X_3114, ID="X_3117", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            central_line(model, X_2, X_39, 2, 39, incident=True)
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            X_184 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A)', ID="X_184", classes=["center", "incident"])
            central_line(model, X_32, X_184, 32, 184, incident=True)
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["center", "incident"])
            X_353 = eval_trilinear_point(model, A, B, C, '(a*(4*a**(4) - 2*b**(4) - 2*c**(4) - b**(2)*c**(2) - 4*a**(2)*b**(2) -4*a**(2)*c**(2)))', ID="X_353", classes=["center", "incident"])
            central_line(model, X_187, X_353, 187, 353, incident=True)
            return promote_point_to_top(model, X_3117)


        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_3117 on the given reference triangle."""
            model = create_model('X_3117 = ISOGONAL CONJUGATE OF TgX(32)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03117(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-03117.json"))
            write_center_svg(
                model_acute,
                here / "x-03117.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3117¶

X₃₁₁₇¶