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X₂₅₂₁¶

RADICAL CENTER OF {BROCARD, BEVAN,MOSES} CIRCLES

X₂₅₂₁ (RADICAL CENTER OF {BROCARD, BEVAN,MOSES} CIRCLES) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2521 = RADICAL CENTER OF {BROCARD, BEVAN,MOSES} CIRCLES."""

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


        def construct_x_02521(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2521 = RADICAL CENTER OF {BROCARD, BEVAN,MOSES} CIRCLES on reference triangle ABC."""
            X_2521 = eval_trilinear_point(model, A, B, C, '(a*(b - c)*(2*(a**(4) + b**(4) + c**(4)) + 3*b*c*(a**(2) + b**(2) + c**(2) + a*b + a*c)))', ID="X_2521", classes=["selected", "target"])
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            X_2031 = eval_trilinear_point(model, A, B, C, '(2*sin(A - 3*omega  ) + (sin(omega)  )*(5*cos(A) + cos(A + 2*omega  )))', ID="X_2031", classes=["center", "incident"])
            central_line(model, X_512, X_2031, 512, 2031, incident=True)
            X_649 = eval_trilinear_point(model, A, B, C, 'a*(b - c)', ID="X_649", classes=["center", "incident"])
            X_2523 = eval_trilinear_point(model, A, B, C, '((b - c)*(b**(2) + c**(2) - a**(2))*(a**(2) + a*(b + c) + (b + c)**(2)))', ID="X_2523", classes=["center", "incident"])
            central_line(model, X_649, X_2523, 649, 2523, incident=True)
            return promote_point_to_top(model, X_2521)


        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_2521 on the given reference triangle."""
            model = create_model('X_2521 = RADICAL CENTER OF {BROCARD, BEVAN,MOSES} CIRCLES')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02521(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-02521.json"))
            write_center_svg(
                model_acute,
                here / "x-02521.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2521¶

X₂₅₂₁¶