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X₃₄₅₃¶

1st SARAGOSSA POINT OF X₁₀

X₃₄₅₃ (1st SARAGOSSA POINT OF X₁₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3453 = 1st SARAGOSSA POINT OF X_10."""

        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_03453(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3453 = 1st SARAGOSSA POINT OF X_10 on reference triangle ABC."""
            X_3453 = eval_trilinear_point(model, A, B, C, '(a/ ((b + c)*( a*(b**(2) + c**(2)) + b**(3) + c**(3) )))', ID="X_3453", classes=["selected", "target"])
            X_60 = eval_trilinear_point(model, A, B, C, '1/(1 + cos(B - C))', ID="X_60", 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_60, X_386, 60, 386, incident=True)
            X_404 = eval_trilinear_point(model, A, B, C, '(b*c*(a + b + c) - a*(b**(2) + c**(2) - a**(2)))', ID="X_404", classes=["center", "incident"])
            X_849 = eval_trilinear_point(model, A, B, C, '(a/(b + c))**(2)', ID="X_849", classes=["center", "incident"])
            central_line(model, X_404, X_849, 404, 849, incident=True)
            X_261 = eval_trilinear_point(model, A, B, C, '(((csc(A))*(sec(B/2 - C/2)))**(2))', ID="X_261", classes=["center", "incident"])
            X_1078 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(2)*c**(2) + c**(2)*a**(2) + a**(2)*b**(2) - a**(4)))', ID="X_1078", classes=["center", "incident"])
            central_line(model, X_261, X_1078, 261, 1078, incident=True)
            return promote_point_to_top(model, X_3453)


        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_3453 on the given reference triangle."""
            model = create_model('X_3453 = 1st SARAGOSSA POINT OF X_10')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03453(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-03453.json"))
            write_center_svg(
                model_acute,
                here / "x-03453.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3453¶

X₃₄₅₃¶