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X₂₆₇₀¶

MIDPOINT OF PU(85)

X₂₆₇₀ is the midpoint of pu(85).

X₂₆₇₀ (MIDPOINT OF PU(85)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2670 = MIDPOINT OF PU(85)."""

        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_02670(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2670 = MIDPOINT OF PU(85) on reference triangle ABC."""
            X_2670 = eval_trilinear_point(model, A, B, C, '((b*a**(2)/(b + a) + c*b**(2)/(c + b) + a*c**(2)/(a + c))*c*a/(c + a) + (c*a**(2)/(c + a) + a*b**(2)/(a + b) + b*c**(2)/(b + c))*b*a/(b + a))', ID="X_2670", classes=["selected", "target"])
            X_1084 = eval_trilinear_point(model, A, B, C, 'a**(3)*(b**(2) - c**(2))**(2)', ID="X_1084", classes=["center", "incident"])
            X_1100 = eval_trilinear_point(model, A, B, C, '2*a + b + c', ID="X_1100", classes=["center", "incident"])
            central_line(model, X_1084, X_1100, 1084, 1100, incident=True)
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            X_2653 = eval_trilinear_point(model, A, B, C, '((a/(cos(B) + cos(A)) + b/(cos(C) + cos(B)) + c/(cos(A) + cos(C)))/(cos(C) + cos(A)) + (a/(cos(C) + cos(A)) + b/(cos(A) + cos(B)) + c/(cos(B) + cos(C)))/(cos(B) + cos(A)))', ID="X_2653", classes=["center", "incident"])
            central_line(model, X_511, X_2653, 511, 2653, incident=True)
            X_798 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b**(2) - c**(2))', ID="X_798", classes=["center", "incident"])
            X_2667 = eval_trilinear_point(model, A, B, C, 'c*a/(c + a) + b*a/(b + a)', ID="X_2667", classes=["center", "incident"])
            central_line(model, X_798, X_2667, 798, 2667, incident=True)
            return promote_point_to_top(model, X_2670)


        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_2670 on the given reference triangle."""
            model = create_model('X_2670 = MIDPOINT OF PU(85)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02670(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-02670.json"))
            write_center_svg(
                model_acute,
                here / "x-02670.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2670¶

X₂₆₇₀¶