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X₂₅₁₁¶

RADICAL CENTER OF {NINE-POINT, APOLLONIUS, MOSES} CIRCLES

X₂₅₁₁ (RADICAL CENTER OF {NINE-POINT, APOLLONIUS, MOSES} CIRCLES) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2511 = RADICAL CENTER OF {NINE-POINT, APOLLONIUS, MOSES} 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_02511(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2511 = RADICAL CENTER OF {NINE-POINT, APOLLONIUS, MOSES} CIRCLES on reference triangle ABC."""
            X_2511 = eval_trilinear_point(model, A, B, C, '((b - c)*(b + c)**(2)*(a**(4) - a**(2)*(b - c)**(2) - b**(2)*c**(2)))', ID="X_2511", classes=["selected", "target"])
            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_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            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"])
            central_line(model, X_115, X_804, 115, 804, incident=True)
            X_665 = eval_trilinear_point(model, A, B, C, 'a*((a - b)**(2)*(a + b - c) - (c - a)**(2)*(c + a - b))', ID="X_665", classes=["center", "incident"])
            X_1213 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c)*(2*a + b + c))', ID="X_1213", classes=["center", "incident"])
            central_line(model, X_665, X_1213, 665, 1213, incident=True)
            return promote_point_to_top(model, X_2511)


        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_2511 on the given reference triangle."""
            model = create_model('X_2511 = RADICAL CENTER OF {NINE-POINT, APOLLONIUS, MOSES} CIRCLES')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02511(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-02511.json"))
            write_center_svg(
                model_acute,
                here / "x-02511.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2511¶

X₂₅₁₁¶