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X₁₇₀₅¶

EXSIMILICENTER(BEVAN CIRCLE, BROCARD CIRCLE)

X₁₇₀₅ is the exsimilicenter(Bevan circle, Brocard circle).

X₁₇₀₅ (EXSIMILICENTER(BEVAN CIRCLE, BROCARD CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1705 = EXSIMILICENTER(BEVAN CIRCLE, BROCARD 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,
            incenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01705(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1705 = EXSIMILICENTER(BEVAN CIRCLE, BROCARD CIRCLE) on reference triangle ABC."""
            X_1705 = eval_trilinear_point(model, A, B, C, '(2*cos(A -  omega  ) - e*(1 + cos(A) - cos(B) - cos(C)))', ID="X_1705", 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_182 = eval_trilinear_point(model, A, B, C, 'cos(A-  omega  )', ID="X_182", classes=["center", "incident"])
            central_line(model, X_40, X_182, 40, 182, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_1341 = point_from_barycentrics(model, A, B, C, 0.30653192, 0.35355532, 0.33991277, ID="X_1341", classes=["center", "incident"])
            central_line(model, X_1, X_1341, 1, 1341, 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_1340 = point_from_barycentrics(model, A, B, C, 0.34709524, 0.36700624, 0.28589852, ID="X_1340", classes=["center", "incident"])
            central_line(model, X_165, X_1340, 165, 1340, incident=True)
            return promote_point_to_top(model, X_1705)


        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_1705 on the given reference triangle."""
            model = create_model('X_1705 = EXSIMILICENTER(BEVAN CIRCLE, BROCARD CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01705(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-01705.json"))
            write_center_svg(
                model_acute,
                here / "x-01705.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1705¶

X₁₇₀₅¶