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X₁₉₀¶

YFF PARABOLIC POINT

In unpublished notes, Yff has studied the parabola tangent to sidelines BC, CA, AB and having focus X₁₀₁. If A',B',C' are the respective points of tangency, then the lines AA', BB', CC' concur in X₁₉₀.

X₁₉₀ (YFF PARABOLIC POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_190 = YFF PARABOLIC POINT."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            mittenpunkt_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00190(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_190 = YFF PARABOLIC POINT on reference triangle ABC."""
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_45 = eval_trilinear_point(model, A, B, C, '2*b + 2*c - a', ID="X_45", classes=["center", "incident"])
            central_line(model, X_2, X_45, 2, 45, incident=True)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            central_line(model, X_9, X_75, 9, 75, incident=True)
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_86 = eval_trilinear_point(model, A, B, C, 'b*c/(b + c)', ID="X_86", classes=["center", "incident"])
            central_line(model, X_37, X_86, 37, 86, incident=True)
            return promote_point_to_top(model, X_190)


        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_190 on the given reference triangle."""
            model = create_model('X_190 = YFF PARABOLIC POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00190(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-00190.json"))
            write_center_svg(
                model_acute,
                here / "x-00190.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X190¶

X₁₉₀¶