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X₈₄₃¶

ISOGONAL CONJUGATE OF X₅₄₃

X₈₄₃ (ISOGONAL CONJUGATE OF X₅₄₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_843 = ISOGONAL CONJUGATE OF X_543."""

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


        def construct_x_00843(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_843 = ISOGONAL CONJUGATE OF X_543 on reference triangle ABC."""
            X_352 = eval_trilinear_point(model, A, B, C, '(a*(-a**(4) - b**(4) - c**(4) - 5*b**(2)*c**(2) + 4*a**(2)*b**(2) + 4*a**(2)*c**(2)))', ID="X_352", classes=["center"])
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["center"])
            X_843 = reflection_in_point(model, X_352, X_187, ID="X_843", classes=["selected", "target"], guide=False)
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_110, X_187, 110, 187, incident=True)
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            central_line(model, X_111, X_512, 111, 512, incident=True)
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_525 = eval_trilinear_point(model, A, B, C, '(b*cos(B) - c*cos(C))/a', ID="X_525", classes=["center", "incident"])
            central_line(model, X_99, X_525, 99, 525, incident=True)
            return promote_point_to_top(model, X_843)


        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_843 on the given reference triangle."""
            model = create_model('X_843 = ISOGONAL CONJUGATE OF X_543')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00843(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-00843.json"))
            write_center_svg(
                model_acute,
                here / "x-00843.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X843¶

X₈₄₃¶