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X₃₄₁₉¶

ISOGONAL CONJUGATE OF X₃₄₁₈

X₃₄₁₉ is the isogonal conjugate of X₃₄₁₈.

X₃₄₁₉ (ISOGONAL CONJUGATE OF X₃₄₁₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3419 = ISOGONAL CONJUGATE OF X_3418."""

        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_barycentric_point,
            eval_trilinear_point,
            mittenpunkt_of,
            nagel_point_of,
            nine_point_center_of,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03419(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3419 = ISOGONAL CONJUGATE OF X_3418 on reference triangle ABC."""
            X_3419 = eval_barycentric_point(model, A, B, C, '(a**(4) - a**(3)*(b + c) + a*(b + c)*(b**(2) + c**(2)) - (b**(2) - c**(2))**(2))', ID="X_3419", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            central_line(model, X_4, X_8, 4, 8, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_78 = eval_trilinear_point(model, A, B, C, '1/(1 - sec(A))', ID="X_78", classes=["center", "incident"])
            central_line(model, X_5, X_78, 5, 78, incident=True)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_80 = eval_trilinear_point(model, A, B, C, '1/(1 - 2*cos(A))', ID="X_80", classes=["center", "incident"])
            central_line(model, X_9, X_80, 9, 80, incident=True)
            return promote_point_to_top(model, X_3419)


        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_3419 on the given reference triangle."""
            model = create_model('X_3419 = ISOGONAL CONJUGATE OF X_3418')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03419(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-03419.json"))
            write_center_svg(
                model_acute,
                here / "x-03419.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3419¶

X₃₄₁₉¶