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X₁₄₁₀¶

X₇₃-BETH CONJUGATE OF X₇₃

X₁₄₁₀ (X₇₃-BETH CONJUGATE OF X₇₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1410 = X_73-BETH CONJUGATE OF X_73."""

        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,
            ceva_conjugate,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01410(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1410 = X_73-BETH CONJUGATE OF X_73 on reference triangle ABC."""
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center"])
            X_1042 = eval_trilinear_point(model, A, B, C, '((1 - cos(A))*(cos(B) + cos(C)))', ID="X_1042", classes=["center"])
            X_1410 = ceva_conjugate(model, A, B, C, X_56, X_1042, ID="X_1410", classes=["selected", "target"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_34 = eval_trilinear_point(model, A, B, C, '1 - sec(A)', ID="X_34", classes=["center", "incident"])
            central_line(model, X_25, X_34, 25, 34, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_77 = eval_trilinear_point(model, A, B, C, '1/(1 + sec(A))', ID="X_77", classes=["center", "incident"])
            central_line(model, X_3, X_77, 3, 77, incident=True)
            X_73 = eval_trilinear_point(model, A, B, C, 'sec(B) + sec(C)', ID="X_73", classes=["center", "incident"])
            X_228 = eval_trilinear_point(model, A, B, C, '(sin(2*A))*(sin(B) + sin(C))', ID="X_228", classes=["center", "incident"])
            central_line(model, X_73, X_228, 73, 228, incident=True)
            return promote_point_to_top(model, X_1410)


        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_1410 on the given reference triangle."""
            model = create_model('X_1410 = X_73-BETH CONJUGATE OF X_73')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01410(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-01410.json"))
            write_center_svg(
                model_acute,
                here / "x-01410.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1410¶

X₁₄₁₀¶