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X₁₅₇₄¶

EXSIMILICENTER OF SPIEKER AND MOSES CIRCLES

X₁₅₇₄ is the exsimilicenter of Spieker and moses circles.

X₁₅₇₄ (EXSIMILICENTER OF SPIEKER AND MOSES CIRCLES) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1574 = EXSIMILICENTER OF SPIEKER AND 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,
            nagel_point_of,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01574(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1574 = EXSIMILICENTER OF SPIEKER AND MOSES CIRCLES on reference triangle ABC."""
            X_1574 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2)) - 2*b*c*(b + c)', ID="X_1574", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            central_line(model, X_10, X_39, 10, 39, incident=True)
            X_38 = eval_trilinear_point(model, A, B, C, 'b**(2) + c**(2)', ID="X_38", classes=["center", "incident"])
            X_762 = eval_trilinear_point(model, A, B, C, '(b + c)**(3)', ID="X_762", classes=["center", "incident"])
            central_line(model, X_38, X_762, 38, 762, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_1015 = eval_trilinear_point(model, A, B, C, 'a*(b - c)**(2)', ID="X_1015", classes=["center", "incident"])
            central_line(model, X_8, X_1015, 8, 1015, incident=True)
            return promote_point_to_top(model, X_1574)


        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_1574 on the given reference triangle."""
            model = create_model('X_1574 = EXSIMILICENTER OF SPIEKER AND MOSES CIRCLES')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01574(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-01574.json"))
            write_center_svg(
                model_acute,
                here / "x-01574.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1574¶

X₁₅₇₄¶