← etc / Encyclopedia of Triangle Centers

X₆₄₆¶

BARYCENTRIC MULTIPLIER FOR YFF PARABOLA

X₆₄₆ satisfies the equation X*(incircle) = Yff parabola, where * denotes barycentric multiplication, defined by

X₆₄₆ (BARYCENTRIC MULTIPLIER FOR YFF PARABOLA) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_646 = BARYCENTRIC MULTIPLIER FOR 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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00646(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_646 = BARYCENTRIC MULTIPLIER FOR YFF PARABOLA on reference triangle ABC."""
            X_646 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(a**(2)*(b - c)))', ID="X_646", classes=["selected", "target"])
            X_644 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(b - c))', ID="X_644", classes=["center", "incident"])
            X_645 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(a*(b**(2) - c**(2))))', ID="X_645", classes=["center", "incident"])
            central_line(model, X_644, X_645, 644, 645, incident=True)
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            X_668 = eval_trilinear_point(model, A, B, C, '1/(a**(2)*(b - c))', ID="X_668", classes=["center", "incident"])
            central_line(model, X_190, X_668, 190, 668, incident=True)
            return promote_point_to_top(model, X_646)


        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_646 on the given reference triangle."""
            model = create_model('X_646 = BARYCENTRIC MULTIPLIER FOR YFF PARABOLA')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00646(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-00646.json"))
            write_center_svg(
                model_acute,
                here / "x-00646.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X646¶

X₆₄₆¶