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X₂₆₃₄¶

MIDPOINT OF PU(75)

X₂₆₃₄ is the midpoint of pu(75).

X₂₆₃₄ (MIDPOINT OF PU(75)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2634 = MIDPOINT OF PU(75)."""

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


        def construct_x_02634(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2634 = MIDPOINT OF PU(75) on reference triangle ABC."""
            X_2634 = eval_trilinear_point(model, A, B, C, '((a/(tan(B) - tan(A)) + b/(tan(C) - tan(B)) + c/(tan(A) - tan(C)))/(tan(C) - tan(A)) + (a/(tan(C) - tan(A)) + b/(tan(A) - tan(B)) + c/(tan(B) - tan(C)))/(tan(B) - tan(A)))', ID="X_2634", classes=["selected", "target"])
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_2629 = eval_barycentric_point(model, A, B, C, 'a*(a**(8) - a**(6)*b**(2) - 2*a**(4)*b**(4) + 3*a**(2)*b**(6) - b**(8) - a**(6)*c**(2) + 5*a**(4)*b**(2)*c**(2) - 3*a**(2)*b**(4)*c**(2) - b**(6)*c**(2) - 2*a**(4)*c**(4) - 3*a**(2)*b**(2)*c**(4) + 4*b**(4)*c**(4) + 3*a**(2)*c**(6) - b**(2)*c**(6) - c**(8))', ID="X_2629", classes=["center", "incident"])
            central_line(model, X_9, X_2629, 9, 2629, incident=True)
            X_2631 = eval_trilinear_point(model, A, B, C, '1/(tan(C) - tan(A)) + 1/(tan(B) - tan(A))', ID="X_2631", classes=["center", "incident"])
            X_2632 = eval_trilinear_point(model, A, B, C, '1/(tan(C) - tan(A)) - 1/(tan(B) - tan(A))', ID="X_2632", classes=["center", "incident"])
            central_line(model, X_2631, X_2632, 2631, 2632, incident=True)
            return promote_point_to_top(model, X_2634)


        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_2634 on the given reference triangle."""
            model = create_model('X_2634 = MIDPOINT OF PU(75)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02634(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-02634.json"))
            write_center_svg(
                model_acute,
                here / "x-02634.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2634¶

X₂₆₃₄¶