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X₄₀₀¶

YFF-MALFATTI POINT

In 1997, Yff considered the configuration for the 1st Ajima-Malfatti point, X₁₇₉. He proved that the same tangencies are possible in another way if the circles are not required to lie inside ABC. With tangency points labeled as before, the lines AA', BB', CC' concur in X₄₀₀.

X₄₀₀ (YFF-MALFATTI POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_400 = YFF-MALFATTI POINT."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00400(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_400 = YFF-MALFATTI POINT on reference triangle ABC."""
            X_400 = eval_trilinear_point(model, A, B, C, '(csc(A/4))**(4)', ID="X_400", classes=["selected", "target"])
            return promote_point_to_top(model, X_400)


        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_400 on the given reference triangle."""
            model = create_model('X_400 = YFF-MALFATTI POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00400(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-00400.json"))
            write_center_svg(
                model_acute,
                here / "x-00400.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X400¶

X₄₀₀¶