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X₅₉₂¶

VAN LAMOEN CIRCUMCENTERS POINT

Let P be the point where the line through X₆ parallel to line CA meets line BC, and let Q be the point where the line through X₆ parallel to line AB meets line BC. Let X = X₁₈₂, and let A' be the circumcenter of the triangle PQX. Define B' and C' cyclically. The lines AA', BB', CC' concur in X₅₉₂. (Floor van Lamoen, 1/4/01)

X₅₉₂ (VAN LAMOEN CIRCUMCENTERS POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_592 = VAN LAMOEN CIRCUMCENTERS POINT."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00592(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_592 = VAN LAMOEN CIRCUMCENTERS POINT on reference triangle ABC."""
            X_592 = eval_trilinear_point(model, A, B, C, '(1/(cos(A) + 2*cos(B -  omega  )*cos(C -  omega  )))', ID="X_592", classes=["selected", "target"])
            return promote_point_to_top(model, X_592)


        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_592 on the given reference triangle."""
            model = create_model('X_592 = VAN LAMOEN CIRCUMCENTERS POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00592(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-00592.json"))
            write_center_svg(
                model_acute,
                here / "x-00592.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X592¶

X₅₉₂¶