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X₉₃₁¶

POINT ALCHIBA

X₉₃₁ (POINT ALCHIBA) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_931 = POINT ALCHIBA."""

        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,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00931(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_931 = POINT ALCHIBA on reference triangle ABC."""
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center"])
            X_643 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(b**(2) - c**(2)))', ID="X_643", classes=["center"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center"])
            X_645 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(a*(b**(2) - c**(2))))', ID="X_645", classes=["center"])
            central_line(model, X_101, X_643, 101, 643)
            central_line(model, X_100, X_645, 100, 645)
            X_931 = intersect_lines(model, X_101, X_643, X_100, X_645, ID="X_931", classes=["selected", "target"])
            X_108 = eval_trilinear_point(model, A, B, C, 'a/(sec(B) - sec(C))', ID="X_108", classes=["center", "incident"])
            X_648 = eval_trilinear_point(model, A, B, C, '1/(a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2)))', ID="X_648", classes=["center", "incident"])
            central_line(model, X_108, X_648, 108, 648, incident=True)
            return promote_point_to_top(model, X_931)


        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_931 on the given reference triangle."""
            model = create_model('X_931 = POINT ALCHIBA')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00931(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-00931.json"))
            write_center_svg(
                model_acute,
                here / "x-00931.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X931¶

X₉₃₁¶