← etc / Encyclopedia of Triangle Centers

X₁₅₀₅¶

EXSIMILICENTER OF MOSES AND 2nd LEMOINE CIRCLES

X₁₅₀₅ is the exsimilicenter of moses and 2nd Lemoine circles.

X₁₅₀₅ (EXSIMILICENTER OF MOSES AND 2nd LEMOINE CIRCLES) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1505 = EXSIMILICENTER OF MOSES AND 2nd LEMOINE CIRCLES."""

        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,
            centroid_of,
            ceva_conjugate,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01505(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1505 = EXSIMILICENTER OF MOSES AND 2nd LEMOINE CIRCLES on reference triangle ABC."""
            X_1307 = point_from_barycentrics(model, A, B, C, 1.0003192, 0.51896067, -0.51927991, ID="X_1307", classes=["center"])
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center"])
            X_1505 = ceva_conjugate(model, A, B, C, X_1307, X_512, ID="X_1505", 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_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_589 = eval_trilinear_point(model, A, B, C, '(a/(a**(2) - 4*area ))', ID="X_589", classes=["center", "incident"])
            central_line(model, X_2, X_589, 2, 589, 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_486 = eval_trilinear_point(model, A, B, C, 'sec(A +  pi  /4)', ID="X_486", classes=["center", "incident"])
            central_line(model, X_115, X_486, 115, 486, incident=True)
            return promote_point_to_top(model, X_1505)


        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_1505 on the given reference triangle."""
            model = create_model('X_1505 = EXSIMILICENTER OF MOSES AND 2nd LEMOINE CIRCLES')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01505(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-01505.json"))
            write_center_svg(
                model_acute,
                here / "x-01505.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1505¶

X₁₅₀₅¶