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X₃₇₉₁¶

X₂₈₈₇com[T(-bc, b²)]

X₃₇₉₁ (X₂₈₈₇com[T(-bc, b²)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3791 = X_2887com[T(-bc, b²)]."""

        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,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03791(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3791 = X_2887com[T(-bc, b²)] on reference triangle ABC."""
            X_3791 = eval_barycentric_point(model, A, B, C, '2*a**(3)+(b+c)*a**(2)-b*c*(b+c)', ID="X_3791", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_333 = eval_trilinear_point(model, A, B, C, 'b*c*(b + c - a)/(b + c)', ID="X_333", classes=["center", "incident"])
            central_line(model, X_1, X_333, 1, 333, incident=True)
            X_171 = eval_trilinear_point(model, A, B, C, 'a**(2) + b*c', ID="X_171", classes=["center", "incident"])
            X_239 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2) - b*c)', ID="X_239", classes=["center", "incident"])
            central_line(model, X_171, X_239, 171, 239, incident=True)
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_740 = eval_trilinear_point(model, A, B, C, 'a **(-2)*(b**(1) + c**(1)) - a**(0)*(b **(-1) + c **(-1))', ID="X_740", classes=["center", "incident"])
            central_line(model, X_31, X_740, 31, 740, incident=True)
            return promote_point_to_top(model, X_3791)


        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_3791 on the given reference triangle."""
            model = create_model('X_3791 = X_2887com[T(-bc, b²)]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03791(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-03791.json"))
            write_center_svg(
                model_acute,
                here / "x-03791.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3791¶

X₃₇₉₁¶