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X₉₃₄¶

X₅₁₃-CROSS CONJUGATE OF X₅₇

X₉₃₄ (X₅₁₃-CROSS CONJUGATE OF X₅₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_934 = X_513-CROSS CONJUGATE OF X_57."""

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


        def construct_x_00934(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_934 = X_513-CROSS CONJUGATE OF X_57 on reference triangle ABC."""
            X_934 = eval_trilinear_point(model, A, B, C, '1/((b - c)*(b + c - a)**(2))', ID="X_934", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_103 = eval_trilinear_point(model, A, B, C, 'a/((a - b)*cot(C) + (a - c)*cot(B))', ID="X_103", classes=["center", "incident"])
            central_line(model, X_1, X_103, 1, 103, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            central_line(model, X_7, X_104, 7, 104, incident=True)
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_105 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2) - a*(b + c))', ID="X_105", classes=["center", "incident"])
            central_line(model, X_56, X_105, 56, 105, incident=True)
            return promote_point_to_top(model, X_934)


        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_934 on the given reference triangle."""
            model = create_model('X_934 = X_513-CROSS CONJUGATE OF X_57')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00934(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-00934.json"))
            write_center_svg(
                model_acute,
                here / "x-00934.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X934¶

X₉₃₄¶