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X₂₅₅₁¶

EXSIMILICENTER(SPIEKER CIRCLE, (X₄,2R))

The circle (X₄,2R) is identified at X₂₄₇₄.

X₂₅₅₁ (EXSIMILICENTER(SPIEKER CIRCLE, (X₄,2R))) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2551 = EXSIMILICENTER(SPIEKER CIRCLE, (X_4,2R))."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            mittenpunkt_of,
            nagel_point_of,
            orthocenter_of,
            promote_point_to_top,
            reflection_in_point,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02551(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2551 = EXSIMILICENTER(SPIEKER CIRCLE, (X_4,2R)) on reference triangle ABC."""
            X_1706 = eval_trilinear_point(model, A, B, C, '(b*c*(2*(b + c) - a*(cos(A) - cos(B) - cos(C) + 1)))', ID="X_1706", classes=["center"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center"])
            X_2551 = reflection_in_point(model, X_1706, X_10, ID="X_2551", classes=["selected", "target"], guide=False)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            central_line(model, X_4, X_9, 4, 9, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            central_line(model, X_2, X_12, 2, 12, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_210 = eval_trilinear_point(model, A, B, C, '(b + c)*(b + c - a)', ID="X_210", classes=["center", "incident"])
            central_line(model, X_8, X_210, 8, 210, incident=True)
            return promote_point_to_top(model, X_2551)


        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_2551 on the given reference triangle."""
            model = create_model('X_2551 = EXSIMILICENTER(SPIEKER CIRCLE, (X_4,2R))')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02551(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-02551.json"))
            write_center_svg(
                model_acute,
                here / "x-02551.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2551¶

X₂₅₅₁¶