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X₃₀₃₁¶

INTERSECTION X₁₀X_125∩X₇₄X_573

X₃₀₃₁ = complement of X₃₈₄₈₂

X₃₀₃₁ (INTERSECTION X₁₀X_125∩X₇₄X_573) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3031 = INTERSECTION X_10X_125∩X_74X_573."""

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


        def construct_x_03031(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3031 = INTERSECTION X_10X_125∩X_74X_573 on reference triangle ABC."""
            X_3031 = eval_trilinear_point(model, A, B, C, '(a*(b + c)**(2)*(a**(3) + b**(3) - c**(3) + a**(2)*c - b**(2)*c - a*c**(2))*(a**(3) - b**(3) + c**(3) + a**(2)*b - b*c**(2) - a*b**(2)))', ID="X_3031", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_125 = eval_trilinear_point(model, A, B, C, 'cos(A)*(sin(B - C))**(2)', ID="X_125", classes=["center", "incident"])
            central_line(model, X_10, X_125, 10, 125, incident=True)
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_386 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2) + b*c + c*a + a*b)', ID="X_386", classes=["center", "incident"])
            central_line(model, X_110, X_386, 110, 386, incident=True)
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            X_573 = eval_trilinear_point(model, A, B, C, 'cos(A + U)', ID="X_573", classes=["center", "incident"])
            central_line(model, X_74, X_573, 74, 573, incident=True)
            return promote_point_to_top(model, X_3031)


        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_3031 on the given reference triangle."""
            model = create_model('X_3031 = INTERSECTION X_10X_125∩X_74X_573')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03031(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-03031.json"))
            write_center_svg(
                model_acute,
                here / "x-03031.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3031¶

X₃₀₃₁¶