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X₁₆₈₂¶

INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE)

The exsimilicenter of the incircle and Apollonius circle is X₁₈₁. Also, the triangle A'B'C' formed (as at X₂₀₉₂ by the intersections of the Apollonius circle and the excircles is perspective to the cevian triangle of X₁, and the perspector is X₁₆₈₂. (Paul Yiu, Hyacinthos #8076, 10/01/03)

X₁₆₈₂ (INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1682 = INSIMILICENTER(INCIRCLE, 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,
            incenter_of,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01682(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1682 = INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE) on reference triangle ABC."""
            X_1682 = eval_trilinear_point(model, A, B, C, '(s*cos(A/2) - r*sin(A/2))**(2)', ID="X_1682", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            central_line(model, X_10, X_11, 10, 11, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", 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_1, X_181, 1, 181, incident=True)
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", 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_55, X_386, 55, 386, incident=True)
            return promote_point_to_top(model, X_1682)


        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_1682 on the given reference triangle."""
            model = create_model('X_1682 = INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01682(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-01682.json"))
            write_center_svg(
                model_acute,
                here / "x-01682.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1682¶

X₁₆₈₂¶