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X₂₆₄₅¶

MIDPOINT OF PU(79)

X₂₆₄₅ is the midpoint of pu(79).

X₂₆₄₅ (MIDPOINT OF PU(79)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2645 = MIDPOINT OF PU(79)."""

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


        def construct_x_02645(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2645 = MIDPOINT OF PU(79) on reference triangle ABC."""
            X_2645 = eval_trilinear_point(model, A, B, C, '((a/(cot(B) - cot(A)) + b/(cot(C) - cot(B)) + c/(cot(A) - cot(C)))/(cot(C) - cot(A)) + (a/(cot(C) - cot(A)) + b/(cot(A) - cot(B)) + c/(cot(B) - cot(C)))/(cot(B) - cot(A)))', ID="X_2645", classes=["selected", "target"])
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_2640 = eval_trilinear_point(model, A, B, C, '(cot(A) - cot(B))*(cot(A) - cot(C)) - (cot(B) - cot(C))**(2)', ID="X_2640", classes=["center", "incident"])
            central_line(model, X_9, X_2640, 9, 2640, incident=True)
            X_2642 = eval_trilinear_point(model, A, B, C, '1/(cot(C) - cot(A)) + 1/(cot(B) - cot(A))', ID="X_2642", classes=["center", "incident"])
            X_2643 = eval_trilinear_point(model, A, B, C, '1/(cot(C) - cot(A)) - 1/(cot(B) - cot(A))', ID="X_2643", classes=["center", "incident"])
            central_line(model, X_2642, X_2643, 2642, 2643, incident=True)
            return promote_point_to_top(model, X_2645)


        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_2645 on the given reference triangle."""
            model = create_model('X_2645 = MIDPOINT OF PU(79)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02645(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-02645.json"))
            write_center_svg(
                model_acute,
                here / "x-02645.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2645¶

X₂₆₄₅¶