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X₂₆₀₉¶

MIDPOINT OF PU(70)

X₂₆₀₉ is the midpoint of pu(70).

X₂₆₀₉ (MIDPOINT OF PU(70)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2609 = MIDPOINT OF PU(70)."""

        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_02609(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2609 = MIDPOINT OF PU(70) on reference triangle ABC."""
            X_2609 = eval_trilinear_point(model, A, B, C, '((a*sin(B - A) + b*sin(C - B) + c*sin(A - C))*sin(C - A) + (a*sin(C - A) + b*sin(A - B) + c*sin(B - C))*sin(B - A))', ID="X_2609", classes=["selected", "target"])
            X_2245 = eval_trilinear_point(model, A, B, C, '(sin(A) + sin(B) + sin(C))*cos(A) - (cos(A) + cos(B) + cos(C))*sin(A)', ID="X_2245", classes=["center", "incident"])
            X_2605 = eval_trilinear_point(model, A, B, C, '(sin(C- A) - sin(B - A))', ID="X_2605", classes=["center", "incident"])
            central_line(model, X_2245, X_2605, 2245, 2605, incident=True)
            return promote_point_to_top(model, X_2609)


        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_2609 on the given reference triangle."""
            model = create_model('X_2609 = MIDPOINT OF PU(70)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02609(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-02609.json"))
            write_center_svg(
                model_acute,
                here / "x-02609.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2609¶

X₂₆₀₉¶