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X₃₂₃₄¶

VERTEX OF THE INSCRIBED YFF PARABOLA

Yff parabola animated over the 3-periodics in an elliptic billiard (i.e., the circumconic with center X₉. Contributed by Dan Reznik, February 12, 2020.

X₃₂₃₄ (VERTEX OF THE INSCRIBED YFF PARABOLA) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3234 = VERTEX OF THE INSCRIBED YFF PARABOLA."""

        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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03234(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3234 = VERTEX OF THE INSCRIBED YFF PARABOLA on reference triangle ABC."""
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center"])
            X_2398 = point_from_barycentrics(model, A, B, C, -1.2222222, 0.33333333, 1.8888889, ID="X_2398", classes=["center"])
            X_3234 = ceva_conjugate(model, A, B, C, X_190, X_2398, ID="X_3234", classes=["selected", "target"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            X_514 = eval_trilinear_point(model, A, B, C, '(b - c)/a', ID="X_514", classes=["center", "incident"])
            central_line(model, X_101, X_514, 101, 514, incident=True)
            X_118 = point_from_barycentrics(model, A, B, C, 0.28918651, -0.056547619, 0.76736111, ID="X_118", classes=["center", "incident"])
            X_516 = eval_trilinear_point(model, A, B, C, 'b*c*((a - b)*cot(C) + (a - c)*cot(B))', ID="X_516", classes=["center", "incident"])
            central_line(model, X_118, X_516, 118, 516, incident=True)
            X_1633 = eval_trilinear_point(model, A, B, C, '((a**(2) + b**(2) + c**(2) - 2*b*c)/(b - c))', ID="X_1633", classes=["center", "incident"])
            X_2736 = point_from_barycentrics(model, A, B, C, 0.10416667, 1.075, -0.17916667, ID="X_2736", classes=["center", "incident"])
            central_line(model, X_1633, X_2736, 1633, 2736, incident=True)
            return promote_point_to_top(model, X_3234)


        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_3234 on the given reference triangle."""
            model = create_model('X_3234 = VERTEX OF THE INSCRIBED YFF PARABOLA')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03234(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-03234.json"))
            write_center_svg(
                model_acute,
                here / "x-03234.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3234¶

X₃₂₃₄¶