← etc / Encyclopedia of Triangle Centers

X₂₀₃₅¶

INSIMILICENTER(MOSES CIRCLE, 1st LEMOINE CIRCLE)

X₂₀₃₅ is the insimilicenter(moses circle, 1st Lemoine circle).

X₂₀₃₅ (INSIMILICENTER(MOSES CIRCLE, 1st LEMOINE CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2035 = INSIMILICENTER(MOSES CIRCLE, 1st LEMOINE 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_02035(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2035 = INSIMILICENTER(MOSES CIRCLE, 1st LEMOINE CIRCLE) on reference triangle ABC."""
            X_2035 = eval_trilinear_point(model, A, B, C, '(sin(A) + sin(A +  omega  ) - sin(A - 2*omega  ))', ID="X_2035", 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_1015 = eval_trilinear_point(model, A, B, C, 'a*(b - c)**(2)', ID="X_1015", classes=["center", "incident"])
            X_1672 = eval_trilinear_point(model, A, B, C, '1 + cos(A -  omega  )', ID="X_1672", classes=["center", "incident"])
            central_line(model, X_1015, X_1672, 1015, 1672, incident=True)
            X_1500 = eval_trilinear_point(model, A, B, C, 'a*(b + c)**(2)', ID="X_1500", classes=["center", "incident"])
            X_1673 = eval_trilinear_point(model, A, B, C, '1 - cos(A -  omega  )', ID="X_1673", classes=["center", "incident"])
            central_line(model, X_1500, X_1673, 1500, 1673, incident=True)
            return promote_point_to_top(model, X_2035)


        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_2035 on the given reference triangle."""
            model = create_model('X_2035 = INSIMILICENTER(MOSES CIRCLE, 1st LEMOINE CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02035(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-02035.json"))
            write_center_svg(
                model_acute,
                here / "x-02035.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2035¶

X₂₀₃₅¶