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X₂₈₅₇¶

SM(X₉₈, X₁₁₀)

X₂₈₅₇ (SM(X₉₈, X₁₁₀)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2857 = SM(X_98, X_110)."""

        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_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02857(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2857 = SM(X_98, X_110) on reference triangle ABC."""
            X_2857 = eval_barycentric_point(model, A, B, C, '(a**(6)*(b**(2) + c**(2)) - 2*a**(4)*(b**(4) + c**(4)) + a**(2)*(b**(6) + c**(6)) + b**(2)*c**(2)*(b**(2) - c**(2))**(2)) / (a**(6)*(b**(2) + c**(2)) - a**(4)*(b**(2) + c**(2))**(2) + a**(2)*(b**(6) + c**(6)) - (b**(2) - c**(2))**(2)*(b**(2) - b*c + c**(2))*(b**(2) + b*c + c**(2)))', ID="X_2857", classes=["selected", "target"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            X_297 = eval_trilinear_point(model, A, B, C, 'csc(2*A)*cos(A +  omega  )', ID="X_297", classes=["center", "incident"])
            central_line(model, X_112, X_297, 112, 297, incident=True)
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_325 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)', ID="X_325", classes=["center", "incident"])
            central_line(model, X_110, X_325, 110, 325, incident=True)
            X_183 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)*cos(A-  omega  )', ID="X_183", classes=["center", "incident"])
            X_476 = eval_trilinear_point(model, A, B, C, '1/((1 + 2*cos(2*A))*sin(B - C))', ID="X_476", classes=["center", "incident"])
            central_line(model, X_183, X_476, 183, 476, incident=True)
            return promote_point_to_top(model, X_2857)


        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_2857 on the given reference triangle."""
            model = create_model('X_2857 = SM(X_98, X_110)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02857(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-02857.json"))
            write_center_svg(
                model_acute,
                here / "x-02857.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2857¶

X₂₈₅₇¶