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X₄₇₈¶

CENTER OF YIU CONIC

Center of the Yiu conic, which passes through the points outside the circumcircle at which the excircles of ABC are tangent to the sidelines of ABC. See Paul Yiu’s

X₄₇₈ (CENTER OF YIU CONIC) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_478 = CENTER OF YIU CONIC."""

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


        def construct_x_00478(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_478 = CENTER OF YIU CONIC on reference triangle ABC."""
            X_478 = eval_trilinear_point(model, A, B, C, 'a*(a**(4) - 2*a*b*c*(b + c - a) - (b**(2) - c**(2))**(2))/(b + c - a)', ID="X_478", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            central_line(model, X_6, X_19, 6, 19, incident=True)
            X_222 = eval_trilinear_point(model, A, B, C, 'cos(A)*tan(A/2)', ID="X_222", classes=["center", "incident"])
            X_226 = eval_trilinear_point(model, A, B, C, '(csc(A))*(cos(B) + cos(C))', ID="X_226", classes=["center", "incident"])
            central_line(model, X_222, X_226, 222, 226, incident=True)
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            X_573 = eval_trilinear_point(model, A, B, C, 'cos(A + U)', ID="X_573", classes=["center", "incident"])
            central_line(model, X_109, X_573, 109, 573, incident=True)
            return promote_point_to_top(model, X_478)


        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_478 on the given reference triangle."""
            model = create_model('X_478 = CENTER OF YIU CONIC')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00478(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-00478.json"))
            write_center_svg(
                model_acute,
                here / "x-00478.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X478¶

X₄₇₈¶