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X₁₆₉₅¶

INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE)

The exsimilicenter of the Bevan and Apollonius circles is X₄₃.

X₁₆₉₅ (INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1695 = INSIMILICENTER(BEVAN 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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01695(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1695 = INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE) on reference triangle ABC."""
            X_939 = eval_trilinear_point(model, A, B, C, '(a/(a**(4) - 2*a**(3)*(b + c) - 4*a**(2)*b*c + (b - c)*(b**(2) - c**(2))*(2*a - b - c)))', ID="X_939", classes=["center"])
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center"])
            X_1695 = ceva_conjugate(model, A, B, C, X_939, X_55, ID="X_1695", classes=["selected", "target"])
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_43 = eval_trilinear_point(model, A, B, C, 'a*b + a*c - b*c', ID="X_43", classes=["center", "incident"])
            central_line(model, X_40, X_43, 40, 43, incident=True)
            X_165 = eval_trilinear_point(model, A, B, C, 'tan(B/2) + tan(C/2) - tan(A/2)', ID="X_165", classes=["center", "incident"])
            X_386 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2) + b*c + c*a + a*b)', ID="X_386", classes=["center", "incident"])
            central_line(model, X_165, X_386, 165, 386, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_573 = eval_trilinear_point(model, A, B, C, 'cos(A + U)', ID="X_573", classes=["center", "incident"])
            central_line(model, X_1, X_573, 1, 573, incident=True)
            return promote_point_to_top(model, X_1695)


        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_1695 on the given reference triangle."""
            model = create_model('X_1695 = INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01695(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-01695.json"))
            write_center_svg(
                model_acute,
                here / "x-01695.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1695¶

X₁₆₉₅¶