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X₁₈₀¶

2nd AJIMA-MALFATTI POINT

Let A″,B″,C″ be the excenters of ABC, and let A',B',C' be as in the construction of X₁₇₉. The lines A'A″,B'B″,B'B″ concur in X₁₈₀. Trilinears are found in Yff’s unpublished notes. See X₁₇₉.

X₁₈₀ (2nd AJIMA-MALFATTI POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_180 = 2nd AJIMA-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 (
            central_line,
            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_00180(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_180 = 2nd AJIMA-MALFATTI POINT on reference triangle ABC."""
            X_180 = point_from_barycentrics(model, A, B, C, 0.24914054, 0.32064866, 0.4302108, ID="X_180", classes=["selected", "target"])
            X_173 = eval_trilinear_point(model, A, B, C, 'cos(B/2) + cos(C/2) - cos(A/2)', ID="X_173", classes=["center", "incident"])
            X_483 = eval_trilinear_point(model, A, B, C, '(sec(A/4))**(2)', ID="X_483", classes=["center", "incident"])
            central_line(model, X_173, X_483, 173, 483, incident=True)
            return promote_point_to_top(model, X_180)


        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_180 on the given reference triangle."""
            model = create_model('X_180 = 2nd AJIMA-MALFATTI POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00180(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-00180.json"))
            write_center_svg(
                model_acute,
                here / "x-00180.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X180¶

X₁₈₀¶