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X₂₈₀₂¶

ISOGONAL CONJUGATE OF X₂₇₁₈

X₂₈₀₂ is the isogonal conjugate of X₂₇₁₈.

X₂₈₀₂ (ISOGONAL CONJUGATE OF X₂₇₁₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2802 = ISOGONAL CONJUGATE OF X_2718."""

        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,
            feuerbach_point_of,
            incenter_of,
            isogonal_conjugate,
            nagel_point_of,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02802(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2802 = ISOGONAL CONJUGATE OF X_2718 on reference triangle ABC."""
            X_2718 = eval_trilinear_point(model, A, B, C, '(1/(b**(3) + c**(3) - a**(2)*b - a**(2)*c - 2*b**(2)*c - 2*b*c**(2) + 4*a*b*c))', ID="X_2718", classes=["center"])
            X_2802 = isogonal_conjugate(model, A, B, C, X_2718, ID="X_2802", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            central_line(model, X_10, X_11, 10, 11, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", 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_8, X_80, 8, 80, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_88 = eval_trilinear_point(model, A, B, C, '1/(b + c - 2*a)', ID="X_88", classes=["center", "incident"])
            central_line(model, X_1, X_88, 1, 88, incident=True)
            return promote_point_to_top(model, X_2802)


        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_2802 on the given reference triangle."""
            model = create_model('X_2802 = ISOGONAL CONJUGATE OF X_2718')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02802(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-02802.json"))
            write_center_svg(
                model_acute,
                here / "x-02802.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2802¶

X₂₈₀₂¶