← etc / Encyclopedia of Triangle Centers

X₂₅₀₆¶

RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, 2nd LEMOINE CIRCLE}

X₂₅₀₆ = midpoint of X₂₄₈₉ in X₂₅₁₉

X₂₅₀₆ (RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, 2nd LEMOINE CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2506 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, 2nd LEMOINE 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,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02506(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2506 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, 2nd LEMOINE CIRCLE} on reference triangle ABC."""
            X_2506 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))*(a**(6) + (b**(2) + c**(2))*(a**(4) - b**(4) + 4*b**(2)*c**(2) - c**(4)) - a**(2)*(b**(4) + 4*b**(2)*c**(2) + c**(4))))', ID="X_2506", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            central_line(model, X_6, X_512, 6, 512, 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_2485 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))*(b**(4) + c**(4) - a**(4)))', ID="X_2485", classes=["center", "incident"])
            central_line(model, X_525, X_2485, 525, 2485, incident=True)
            X_2489 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))/(b**(2) + c**(2) - a**(2)))', ID="X_2489", classes=["center", "incident"])
            X_2519 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2))*(a**(4) + b**(4) + c**(4) + 2*a**(2)*b**(2) + 2*a**(2)*c**(2) - 6*b**(2)*c**(2)))', ID="X_2519", classes=["center", "incident"])
            central_line(model, X_2489, X_2519, 2489, 2519, incident=True)
            return promote_point_to_top(model, X_2506)


        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_2506 on the given reference triangle."""
            model = create_model('X_2506 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, 2nd LEMOINE CIRCLE}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02506(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-02506.json"))
            write_center_svg(
                model_acute,
                here / "x-02506.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2506¶

X₂₅₀₆¶