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X₂₄₇₄¶

RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X₄,2R)} CIRCLES

The titular notation (X₄,2R) means the circle with center X₄ and radius 2R, where R denotes the circumradius of triangle ABC.

X₂₄₇₄ (RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X₄,2R)} CIRCLES) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X_4,2R)} 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_02474(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X_4,2R)} CIRCLES on reference triangle ABC."""
            X_2474 = eval_trilinear_point(model, A, B, C, '(a*(b**(4) - c**(4))*(a**(4) + b**(4) + c**(4) + 2*a**(2)*b**(2) + 2*a**(2)*c**(2) - 2*b**(2)*c**(2)))', ID="X_2474", classes=["selected", "target"])
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            X_1570 = eval_trilinear_point(model, A, B, C, 'a*(cot(A) + cot(omega)  - 4*tan(omega)  )', ID="X_1570", classes=["center", "incident"])
            central_line(model, X_512, X_1570, 512, 1570, incident=True)
            X_525 = eval_trilinear_point(model, A, B, C, '(b*cos(B) - c*cos(C))/a', ID="X_525", classes=["center", "incident"])
            X_2514 = 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_2514", classes=["center", "incident"])
            central_line(model, X_525, X_2514, 525, 2514, incident=True)
            X_826 = eval_trilinear_point(model, A, B, C, 'a **(-1)*(b**(4) - c**(4)) + a**(3)*(b**(0) - c**(0))', ID="X_826", classes=["center", "incident"])
            X_2518 = eval_trilinear_point(model, A, B, C, '(a*(b**(4) - c**(4))*(2*a**(4) + 2*b**(4) + 2*c**(4) - 3*b**(2)*c**(2)))', ID="X_2518", classes=["center", "incident"])
            central_line(model, X_826, X_2518, 826, 2518, incident=True)
            return promote_point_to_top(model, X_2474)


        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_2474 on the given reference triangle."""
            model = create_model('X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X_4,2R)} CIRCLES')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02474(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-02474.json"))
            write_center_svg(
                model_acute,
                here / "x-02474.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2474¶

X₂₄₇₄¶