← etc / Encyclopedia of Triangle Centers

X₂₅₆₁¶

EXSIMILICENTER(2nd LEMOINE CIRCLE, 2nd BROCARD CIRCLE)

X₂₅₆₁ is the exsimilicenter(2nd Lemoine circle, 2nd Brocard circle).

X₂₅₆₁ (EXSIMILICENTER(2nd LEMOINE CIRCLE, 2nd BROCARD CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2561 = EXSIMILICENTER(2nd LEMOINE CIRCLE, 2nd 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02561(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2561 = EXSIMILICENTER(2nd LEMOINE CIRCLE, 2nd BROCARD CIRCLE) on reference triangle ABC."""
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_485 = eval_trilinear_point(model, A, B, C, 'sec(A -  pi  /4)', ID="X_485", classes=["center"])
            X_2566 = eval_trilinear_point(model, A, B, C, '(cos(A) + e*cos(B - C))', ID="X_2566", classes=["center"])
            central_line(model, X_3, X_6, 3, 6)
            central_line(model, X_485, X_2566, 485, 2566)
            X_2561 = intersect_lines(model, X_3, X_6, X_485, X_2566, ID="X_2561", classes=["selected", "target"])
            X_486 = eval_trilinear_point(model, A, B, C, 'sec(A +  pi  /4)', ID="X_486", classes=["center", "incident"])
            X_2567 = eval_trilinear_point(model, A, B, C, '(cos(A) - e*cos(B - C))', ID="X_2567", classes=["center", "incident"])
            central_line(model, X_486, X_2567, 486, 2567, incident=True)
            return promote_point_to_top(model, X_2561)


        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_2561 on the given reference triangle."""
            model = create_model('X_2561 = EXSIMILICENTER(2nd LEMOINE CIRCLE, 2nd BROCARD CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02561(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-02561.json"))
            write_center_svg(
                model_acute,
                here / "x-02561.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2561¶

X₂₅₆₁¶