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X₂₅₃₄¶

INSIMILICENTER(INCIRCLE, SPIEKER RADICAL CIRCLE)

The Spieker radical circle, with center X₁₀ and radius d/2, is introduced in

X₂₅₃₄ (INSIMILICENTER(INCIRCLE, SPIEKER RADICAL CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2534 = INSIMILICENTER(INCIRCLE, SPIEKER RADICAL 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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            feuerbach_point_of,
            incenter_of,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02534(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2534 = INSIMILICENTER(INCIRCLE, SPIEKER RADICAL CIRCLE) on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center"])
            X_2540 = point_from_barycentrics(model, A, B, C, 0.30492756, 0.31085991, 0.38421252, ID="X_2540", classes=["center"])
            central_line(model, X_1, X_2, 1, 2)
            central_line(model, X_11, X_2540, 11, 2540)
            X_2534 = intersect_lines(model, X_1, X_2, X_11, X_2540, ID="X_2534", classes=["selected", "target"])
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            X_2541 = point_from_barycentrics(model, A, B, C, 0.23292563, 0.28205914, 0.48501523, ID="X_2541", classes=["center", "incident"])
            central_line(model, X_12, X_2541, 12, 2541, incident=True)
            return promote_point_to_top(model, X_2534)


        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_2534 on the given reference triangle."""
            model = create_model('X_2534 = INSIMILICENTER(INCIRCLE, SPIEKER RADICAL CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02534(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-02534.json"))
            write_center_svg(
                model_acute,
                here / "x-02534.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2534¶

X₂₅₃₄¶