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X₂₅₀₉¶

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

X₂₅₀₉ = midpoint of X₆₆₁ and X₂₄₈₄

X₂₅₀₉ (RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, APOLLONIUS CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2509 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, APOLLONIUS 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,
            midpoint,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02509(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2509 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, APOLLONIUS CIRCLE} on reference triangle ABC."""
            X_661 = eval_trilinear_point(model, A, B, C, 'cot(B) - cot(C)', ID="X_661", classes=["center"])
            X_2484 = eval_trilinear_point(model, A, B, C, '(a*(b - c)*(a**(2) + b**(2) + c**(2) + 2*b*c))', ID="X_2484", classes=["center"])
            X_2509 = midpoint(model, X_661, X_2484, ID="X_2509", classes=["selected", "target"], guide=False)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_521 = eval_trilinear_point(model, A, B, C, '(sec(B) - sec(C))*(csc(A))', ID="X_521", classes=["center", "incident"])
            central_line(model, X_6, X_521, 6, 521, incident=True)
            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_905 = eval_trilinear_point(model, A, B, C, '(b - c)*cot(A)', ID="X_905", classes=["center", "incident"])
            X_918 = eval_barycentric_point(model, A, B, C, '((b - c)*(b**(2) + c**(2) -a*b - a*c))', ID="X_918", classes=["center", "incident"])
            central_line(model, X_905, X_918, 905, 918, incident=True)
            return promote_point_to_top(model, X_2509)


        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_2509 on the given reference triangle."""
            model = create_model('X_2509 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, APOLLONIUS CIRCLE}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02509(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-02509.json"))
            write_center_svg(
                model_acute,
                here / "x-02509.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2509¶

X₂₅₀₉¶