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X₂₆₅₇¶

MIDPOINT OF PU(82)

X₂₆₅₇ is the midpoint of pu(82).

X₂₆₅₇ (MIDPOINT OF PU(82)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2657 = MIDPOINT OF PU(82)."""

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


        def construct_x_02657(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2657 = MIDPOINT OF PU(82) on reference triangle ABC."""
            X_2657 = 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_2657", classes=["selected", "target"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_2190 = eval_trilinear_point(model, A, B, C, 'sec(A)*sec(B - C)', ID="X_2190", classes=["center", "incident"])
            central_line(model, X_37, X_2190, 37, 2190, incident=True)
            X_652 = eval_trilinear_point(model, A, B, C, 'sec(B) - sec(C)', ID="X_652", classes=["center", "incident"])
            X_2654 = eval_trilinear_point(model, A, B, C, '2*sec(A) + sec(B) + sec(C)', ID="X_2654", classes=["center", "incident"])
            central_line(model, X_652, X_2654, 652, 2654, incident=True)
            return promote_point_to_top(model, X_2657)


        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_2657 on the given reference triangle."""
            model = create_model('X_2657 = MIDPOINT OF PU(82)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02657(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-02657.json"))
            write_center_svg(
                model_acute,
                here / "x-02657.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2657¶

X₂₆₅₇¶