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X₂₀₃₃¶

INSIMILICENTER(MOSES CIRCLE, BROCARD CIRCLE)

X₂₀₃₃ is the insimilicenter(moses circle, Brocard circle).

X₂₀₃₃ (INSIMILICENTER(MOSES CIRCLE, BROCARD CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2033 = INSIMILICENTER(MOSES 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02033(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2033 = INSIMILICENTER(MOSES CIRCLE, BROCARD CIRCLE) on reference triangle ABC."""
            X_2033 = eval_trilinear_point(model, A, B, C, '(sin(A) + e*sin(A +  omega  ) - sin(A - 2*omega  ))', ID="X_2033", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_1348 = eval_trilinear_point(model, A, B, C, 'e*cos(B - C) + cos(A -  omega  )', ID="X_1348", classes=["center", "incident"])
            central_line(model, X_115, X_1348, 115, 1348, incident=True)
            X_1349 = eval_trilinear_point(model, A, B, C, 'e*cos(B - C) - cos(A -  omega  )', ID="X_1349", classes=["center", "incident"])
            X_1506 = eval_trilinear_point(model, A, B, C, 'b*c*((b**(2) - c**(2))**(2) - 2*a**(2)*(b**(2) + c**(2)))', ID="X_1506", classes=["center", "incident"])
            central_line(model, X_1349, X_1506, 1349, 1506, incident=True)
            return promote_point_to_top(model, X_2033)


        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_2033 on the given reference triangle."""
            model = create_model('X_2033 = INSIMILICENTER(MOSES CIRCLE, BROCARD CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02033(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-02033.json"))
            write_center_svg(
                model_acute,
                here / "x-02033.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2033¶

X₂₀₃₃¶