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X₃₇₈₅¶

X₂₅₄₈com[INVERSE(nT(a², a² + b²))]

X₃₇₈₅ (X₂₅₄₈com[INVERSE(nT(a², a² + b²))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3785 = X_2548com[INVERSE(nT(a², a² + b²))]."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            anticomplement,
            central_line,
            centroid_of,
            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_03785(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3785 = X_2548com[INVERSE(nT(a², a² + b²))] on reference triangle ABC."""
            X_2548 = eval_trilinear_point(model, A, B, C, '(2*cos(B)*cos(C) + sin(A +  omega  )*csc(omega) )', ID="X_2548", classes=["center"])
            X_3785 = anticomplement(model, A, B, C, X_2548, ID="X_3785", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            central_line(model, X_2, X_32, 2, 32, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_3, X_69, 3, 69, incident=True)
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            central_line(model, X_20, X_76, 20, 76, incident=True)
            return promote_point_to_top(model, X_3785)


        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_3785 on the given reference triangle."""
            model = create_model('X_3785 = X_2548com[INVERSE(nT(a², a² + b²))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03785(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-03785.json"))
            write_center_svg(
                model_acute,
                here / "x-03785.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3785¶

X₃₇₈₅¶