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X₂₄₉₄¶

RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 1st LEMOINE CIRCLE}

X₂₄₉₄ = midpoint of X₂₄₈₈ and X₂₄₉₅

X₂₄₉₄ (RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 1st LEMOINE CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2494 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 1st 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,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02494(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2494 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 1st LEMOINE CIRCLE} on reference triangle ABC."""
            X_2494 = eval_trilinear_point(model, A, B, C, '(a*b**(2)*(a**(2) + b**(2))*(a + c - b)**(2) - a*c**(2)*(a**(2) + c**(2))*(a + b - c)**(2))', ID="X_2494", classes=["selected", "target"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            X_676 = eval_trilinear_point(model, A, B, C, '(b*c*(b - c)*(b**(3) + c**(3) - 2*a**(3) + (b + c)*(a**(2) - b*c)))', ID="X_676", classes=["center", "incident"])
            central_line(model, X_513, X_676, 513, 676, incident=True)
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            X_1691 = eval_trilinear_point(model, A, B, C, 'sin(A - 2*omega  )', ID="X_1691", classes=["center", "incident"])
            central_line(model, X_512, X_1691, 512, 1691, incident=True)
            return promote_point_to_top(model, X_2494)


        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_2494 on the given reference triangle."""
            model = create_model('X_2494 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 1st LEMOINE CIRCLE}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02494(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-02494.json"))
            write_center_svg(
                model_acute,
                here / "x-02494.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2494¶

X₂₄₉₄¶