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X₂₅₁₆¶

RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE}

X₂₅₁₆ = anticomplementary isotomic conjugate of trilinear pole, wrt anticomplementary triangle, of Gergonne line

X₂₅₁₆ (RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE}."""

        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_02516(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} on reference triangle ABC."""
            X_2516 = eval_trilinear_point(model, A, B, C, '((b - c)*(5*a - 3*b -3*c))', ID="X_2516", classes=["selected", "target"])
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center", "incident"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            central_line(model, X_44, X_513, 44, 513, incident=True)
            X_514 = eval_trilinear_point(model, A, B, C, '(b - c)/a', ID="X_514", classes=["center", "incident"])
            X_2487 = eval_trilinear_point(model, A, B, C, '(b*c*(b - c)*((b - c)**(2) + a*b + a*c - 4*a**(2)))', ID="X_2487", classes=["center", "incident"])
            central_line(model, X_514, X_2487, 514, 2487, incident=True)
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center", "incident"])
            X_2490 = eval_trilinear_point(model, A, B, C, '(b*c*(b - c)*(4*a**(2) - 3*a*b - 3*a*c + (b + c)**(2)))', ID="X_2490", classes=["center", "incident"])
            central_line(model, X_522, X_2490, 522, 2490, incident=True)
            return promote_point_to_top(model, X_2516)


        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_2516 on the given reference triangle."""
            model = create_model('X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02516(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-02516.json"))
            write_center_svg(
                model_acute,
                here / "x-02516.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2516¶

X₂₅₁₆¶