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X₂₈₅₅¶

SM(X₇₄, X₉₈)

X₂₈₅₅ (SM(X₇₄, X₉₈)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2855 = SM(X_74, X_98)."""

        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,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02855(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2855 = SM(X_74, X_98) on reference triangle ABC."""
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center"])
            X_325 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)', ID="X_325", classes=["center"])
            X_877 = point_from_barycentrics(model, A, B, C, -0.31137873, 0.061326014, 1.2500527, ID="X_877", classes=["center"])
            X_1304 = eval_trilinear_point(model, A, B, C, '(sin(A))/((tan(B) - tan(C))*(tan(B) + tan(C) - 2*tan(A)))', ID="X_1304", classes=["center"])
            central_line(model, X_74, X_325, 74, 325)
            central_line(model, X_877, X_1304, 877, 1304)
            X_2855 = intersect_lines(model, X_74, X_325, X_877, X_1304, ID="X_2855", classes=["selected", "target"])
            X_2407 = eval_trilinear_point(model, A, B, C, '(csc(C - A)*cos(C) - csc(A - B)*cos(B))*(csc(B - C)/a)**(2)', ID="X_2407", classes=["center", "incident"])
            X_2715 = eval_trilinear_point(model, A, B, C, 'a/((b**(2) - c**(2))*(b**(4) + c**(4) - a**(2)*b**(2) - a**(2)*c**(2)))', ID="X_2715", classes=["center", "incident"])
            central_line(model, X_2407, X_2715, 2407, 2715, incident=True)
            return promote_point_to_top(model, X_2855)


        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_2855 on the given reference triangle."""
            model = create_model('X_2855 = SM(X_74, X_98)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02855(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-02855.json"))
            write_center_svg(
                model_acute,
                here / "x-02855.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2855¶

X₂₈₅₅¶