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X₂₀₅₁¶

EXSIMILICENTER(NINE-POINT CIRCLE, APOLLONIUS CIRCLE)

X₂₀₅₁ is the external center of similitude of the nine-point and Apollonius circles. Trilinears for the internal center, X₁₀, result from g(a,b,c) by changing the “-” just after “cos A″ to “+”. (The two circles are described just before X₁₆₆₂.)

X₂₀₅₁ (EXSIMILICENTER(NINE-POINT CIRCLE, APOLLONIUS CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2051 = EXSIMILICENTER(NINE-POINT 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_trilinear_point,
            feuerbach_point_of,
            isogonal_conjugate,
            nine_point_center_of,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02051(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2051 = EXSIMILICENTER(NINE-POINT CIRCLE, APOLLONIUS CIRCLE) on reference triangle ABC."""
            X_572 = eval_trilinear_point(model, A, B, C, '(cos(A - U))', ID="X_572", classes=["center"])
            X_2051 = isogonal_conjugate(model, A, B, C, X_572, ID="X_2051", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            central_line(model, X_5, X_10, 5, 10, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_181 = eval_trilinear_point(model, A, B, C, 'a*(b + c)**(2)/(b + c - a)', ID="X_181", classes=["center", "incident"])
            central_line(model, X_11, X_181, 11, 181, incident=True)
            X_27 = eval_trilinear_point(model, A, B, C, '(sec(A))/(b + c)', ID="X_27", classes=["center", "incident"])
            X_275 = eval_trilinear_point(model, A, B, C, 'csc(2*A)*sec(B - C)', ID="X_275", classes=["center", "incident"])
            central_line(model, X_27, X_275, 27, 275, incident=True)
            return promote_point_to_top(model, X_2051)


        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_2051 on the given reference triangle."""
            model = create_model('X_2051 = EXSIMILICENTER(NINE-POINT CIRCLE, APOLLONIUS CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02051(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-02051.json"))
            write_center_svg(
                model_acute,
                here / "x-02051.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2051¶

X₂₀₅₁¶