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X₂₄₂₀¶

ISOGONAL CONJUGATE OF X₂₃₉₄

Centers X₂₄₂₀ to X₂₄₄₅, on the cubic K162, are isogonal conjugates of centers X₂₃₉₄ to X₂₄₁₉, which are on the Simson cubic, K010. For details, see the note just before X₂₃₉₄.

X₂₄₂₀ (ISOGONAL CONJUGATE OF X₂₃₉₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2420 = ISOGONAL CONJUGATE OF X_2394."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02420(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2420 = ISOGONAL CONJUGATE OF X_2394 on reference triangle ABC."""
            X_2394 = point_from_barycentrics(model, A, B, C, -0.40056818, 1.1914336, 0.20913462, ID="X_2394", classes=["center"])
            X_2420 = isogonal_conjugate(model, A, B, C, X_2394, ID="X_2420", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            central_line(model, X_110, X_112, 110, 112, incident=True)
            X_249 = eval_trilinear_point(model, A, B, C, '(csc(A))*(csc(B - C))**(2)', ID="X_249", classes=["center", "incident"])
            X_2421 = eval_trilinear_point(model, A, B, C, '(sin(A))*(sin(2*B) + sin(2*C) - 2*(cot(A))*((sin(B))**(2) + (sin(C))**(2)))/(cot(B) - cot(C))', ID="X_2421", classes=["center", "incident"])
            central_line(model, X_249, X_2421, 249, 2421, incident=True)
            return promote_point_to_top(model, X_2420)


        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_2420 on the given reference triangle."""
            model = create_model('X_2420 = ISOGONAL CONJUGATE OF X_2394')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02420(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-02420.json"))
            write_center_svg(
                model_acute,
                here / "x-02420.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2420¶

X₂₄₂₀¶