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X₂₄₅₇¶

RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES

X₂₄₅₇ (RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2457 = RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} 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_02457(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2457 = RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES on reference triangle ABC."""
            X_2457 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(2) - c**(2))*(2*a**(3) + a**(2)*(b + c) - (b + c)*(b - c)**(2) - 2*a*(b**(2) - b*c + c**(2))))', ID="X_2457", classes=["selected", "target"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            X_656 = eval_trilinear_point(model, A, B, C, 'tan(B) - tan(C)', ID="X_656", classes=["center", "incident"])
            central_line(model, X_523, X_656, 523, 656, incident=True)
            X_650 = eval_trilinear_point(model, A, B, C, 'cos(B) - cos(C)', ID="X_650", classes=["center", "incident"])
            X_2529 = eval_trilinear_point(model, A, B, C, '(b*c*(b - c)*(7*a**(2) + a*b + a*c + 2*(b + c)**(2)))', ID="X_2529", classes=["center", "incident"])
            central_line(model, X_650, X_2529, 650, 2529, incident=True)
            return promote_point_to_top(model, X_2457)


        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_2457 on the given reference triangle."""
            model = create_model('X_2457 = RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02457(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-02457.json"))
            write_center_svg(
                model_acute,
                here / "x-02457.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2457¶

X₂₄₅₇¶