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X₂₆₆₁¶

MIDPOINT OF PU(83)

X₂₆₆₁ is the midpoint of pu(83).

X₂₆₆₁ (MIDPOINT OF PU(83)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2661 = MIDPOINT OF PU(83)."""

        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_02661(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2661 = MIDPOINT OF PU(83) on reference triangle ABC."""
            X_2661 = eval_trilinear_point(model, A, B, C, '((a/(sec(B) + sec(A)) + b/(sec(C) + sec(B)) + c/(sec(A) + sec(C)))/(sec(C) + sec(A)) + (a/(sec(C) + sec(A)) + b/(sec(A) + sec(B)) + c/(sec(B) + sec(C)))/(sec(B) + sec(A)))', ID="X_2661", classes=["selected", "target"])
            X_822 = eval_trilinear_point(model, A, B, C, '(sec(B))**(2) - (sec(C))**(2)', ID="X_822", classes=["center", "incident"])
            X_2658 = point_from_barycentrics(model, A, B, C, 0.32414957, 0.38052829, 0.29532214, ID="X_2658", classes=["center", "incident"])
            central_line(model, X_822, X_2658, 822, 2658, incident=True)
            return promote_point_to_top(model, X_2661)


        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_2661 on the given reference triangle."""
            model = create_model('X_2661 = MIDPOINT OF PU(83)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02661(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-02661.json"))
            write_center_svg(
                model_acute,
                here / "x-02661.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2661¶

X₂₆₆₁¶