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X₃₇₈₁¶

X₉com[INVERSE(nT(bc, c²))]

X₃₇₈₁ (X₉com[INVERSE(nT(bc, c²))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3781 = X_9com[INVERSE(nT(bc, c²))]."""

        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,
            circumcenter_of,
            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_03781(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3781 = X_9com[INVERSE(nT(bc, c²))] on reference triangle ABC."""
            X_3781 = eval_barycentric_point(model, A, B, C, '(a**(2)*(b**(2) + c**(2) - a**(2))*(b**(2) + c**(2) + b*c))', ID="X_3781", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center", "incident"])
            central_line(model, X_3, X_48, 3, 48, incident=True)
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            central_line(model, X_69, X_72, 69, 72, incident=True)
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_295 = eval_trilinear_point(model, A, B, C, '(cos(A))/(a**(2) - b*c)', ID="X_295", classes=["center", "incident"])
            central_line(model, X_63, X_295, 63, 295, incident=True)
            return promote_point_to_top(model, X_3781)


        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_3781 on the given reference triangle."""
            model = create_model('X_3781 = X_9com[INVERSE(nT(bc, c²))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03781(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-03781.json"))
            write_center_svg(
                model_acute,
                here / "x-03781.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3781¶

X₃₇₈₁¶