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X₂₄₆₉¶

INSIMILICENTER(ORTHOCENTROIDALCIRCLE, BROCARD CIRCLE)

X₂₄₆₉ is the insimilicenter(orthocentroidalcircle, Brocard circle).

X₂₄₆₉ (INSIMILICENTER(ORTHOCENTROIDALCIRCLE, BROCARD CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2469 = INSIMILICENTER(ORTHOCENTROIDALCIRCLE, 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,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02469(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2469 = INSIMILICENTER(ORTHOCENTROIDALCIRCLE, BROCARD CIRCLE) on reference triangle ABC."""
            X_182 = eval_trilinear_point(model, A, B, C, 'cos(A-  omega  )', ID="X_182", classes=["center"])
            X_381 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) - cos(A)', ID="X_381", classes=["center"])
            X_1668 = eval_trilinear_point(model, A, B, C, 'cos(A -  omega  ) - e*sin(A)', ID="X_1668", classes=["center"])
            X_2465 = eval_trilinear_point(model, A, B, C, '(cos(A) + 4*cos(B)*cos(C) + J*sin(A))', ID="X_2465", classes=["center"])
            central_line(model, X_182, X_381, 182, 381)
            central_line(model, X_1668, X_2465, 1668, 2465)
            X_2469 = intersect_lines(model, X_182, X_381, X_1668, X_2465, ID="X_2469", classes=["selected", "target"])
            X_1669 = eval_trilinear_point(model, A, B, C, 'cos(A -  omega  ) + e*sin(A)', ID="X_1669", classes=["center", "incident"])
            X_2466 = eval_trilinear_point(model, A, B, C, '(cos(A) + 4*cos(B)*cos(C) - J*sin(A))', ID="X_2466", classes=["center", "incident"])
            central_line(model, X_1669, X_2466, 1669, 2466, incident=True)
            return promote_point_to_top(model, X_2469)


        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_2469 on the given reference triangle."""
            model = create_model('X_2469 = INSIMILICENTER(ORTHOCENTROIDALCIRCLE, BROCARD CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02469(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-02469.json"))
            write_center_svg(
                model_acute,
                here / "x-02469.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2469¶

X₂₄₆₉¶