← etc / Encyclopedia of Triangle Centers

X₂₅₀₇¶

RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, GALLATLY CIRCLE}

X₂₅₀₇ = midpoint of X₂₄₈₉ and X₂₅₂₄

X₂₅₀₇ (RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, GALLATLY CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2507 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, GALLATLY 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_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02507(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2507 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, GALLATLY CIRCLE} on reference triangle ABC."""
            X_2507 = eval_trilinear_point(model, A, B, C, '(a*((b**(4) - c**(4))*a**(6) - (b**(8) - c**(8))*a**(2) + 2*b**(4)*c**(4)*(b**(2) - c**(2))))', ID="X_2507", classes=["selected", "target"])
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            X_2024 = eval_trilinear_point(model, A, B, C, 'sin(A) - 3*sin(A - 2*omega  ) - 2*cos(omega)*sin(A + 3*omega  )', ID="X_2024", classes=["center", "incident"])
            central_line(model, X_512, X_2024, 512, 2024, incident=True)
            X_804 = eval_trilinear_point(model, A, B, C, 'a **(-3)*(b**(2) - c**(2)) + a**(1)*(b **(-2) - c **(-2))', ID="X_804", classes=["center", "incident"])
            X_2023 = eval_trilinear_point(model, A, B, C, '(sin(omega)*cos(B - C) - cos(2*omega)*sin(A +  omega  ))', ID="X_2023", classes=["center", "incident"])
            central_line(model, X_804, X_2023, 804, 2023, incident=True)
            X_1194 = eval_trilinear_point(model, A, B, C, '(a*(b**(4) + c**(4) + a**(2)*b**(2) + a**(2)*c**(2)))', ID="X_1194", classes=["center", "incident"])
            X_1637 = eval_barycentric_point(model, A, B, C, 'tan(A)*(tan(B) - tan(C))*(tan(B) + tan(C) - 2*tan(A))', ID="X_1637", classes=["center", "incident"])
            central_line(model, X_1194, X_1637, 1194, 1637, incident=True)
            return promote_point_to_top(model, X_2507)


        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_2507 on the given reference triangle."""
            model = create_model('X_2507 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, GALLATLY CIRCLE}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02507(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-02507.json"))
            write_center_svg(
                model_acute,
                here / "x-02507.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2507¶

X₂₅₀₇¶