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X₁₁₅₃¶

CENTER OF THE VAN LAMOEN CIRCLE

A triangle is divided by its three medians into 6 smaller triangles. The circumcenters of these smaller triangles are concyclic. Their circle, the Van Lamoen circle, is introduced in

X₁₁₅₃ (CENTER OF THE VAN LAMOEN CIRCLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1153 = CENTER OF THE VAN LAMOEN 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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01153(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1153 = CENTER OF THE VAN LAMOEN CIRCLE on reference triangle ABC."""
            X_1153 = eval_trilinear_point(model, A, B, C, 'b*c*(13*a**(2)*(b**(2) + c**(2)) + 10*b**(2)*c**(2) - 10*a**(4) - 4*b**(4) - 4*c**(4))', ID="X_1153", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["center", "incident"])
            central_line(model, X_2, X_187, 2, 187, incident=True)
            X_140 = eval_trilinear_point(model, A, B, C, '2*cos(A) + cos(B - C)', ID="X_140", classes=["center", "incident"])
            X_524 = eval_trilinear_point(model, A, B, C, '(2*a**(2) - b**(2) - c**(2))/a', ID="X_524", classes=["center", "incident"])
            central_line(model, X_140, X_524, 140, 524, incident=True)
            X_543 = eval_barycentric_point(model, A, B, C, '2*a**(4) - b**(4) - c**(4) - 2*a**(2)*b**(2) - 2*a**(2)*c**(2) + 4*b**(2)*c**(2)', ID="X_543", classes=["center", "incident"])
            X_549 = eval_trilinear_point(model, A, B, C, 'cos(B - C) + 4*cos(A)', ID="X_549", classes=["center", "incident"])
            central_line(model, X_543, X_549, 543, 549, incident=True)
            return promote_point_to_top(model, X_1153)


        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_1153 on the given reference triangle."""
            model = create_model('X_1153 = CENTER OF THE VAN LAMOEN CIRCLE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01153(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-01153.json"))
            write_center_svg(
                model_acute,
                here / "x-01153.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1153¶

X₁₁₅₃¶