← etc / Encyclopedia of Triangle Centers

X₄₉₃¶

1st VAN LAMOEN HOMOTHETIC CENTER

X₄₉₃ is a homothetic center of triangles associated with squares that circumscribe ABC. For details, see Vierkanten in een driehoek: 4. Ingeschreven vierkanten (Floor van Lamoen, 4/27/98)

X₄₉₃ (1st VAN LAMOEN HOMOTHETIC CENTER) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_493 = 1st VAN LAMOEN HOMOTHETIC CENTER."""

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


        def construct_x_00493(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_493 = 1st VAN LAMOEN HOMOTHETIC CENTER on reference triangle ABC."""
            X_493 = eval_trilinear_point(model, A, B, C, '1/(sin(A) + sin(B)*sin(C))', ID="X_493", classes=["selected", "target"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_371 = eval_trilinear_point(model, A, B, C, 'cos(A -  pi  /4)', ID="X_371", classes=["center", "incident"])
            central_line(model, X_25, X_371, 25, 371, incident=True)
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            X_494 = eval_trilinear_point(model, A, B, C, '1/(sin(A) - sin(B)*sin(C))', ID="X_494", classes=["center", "incident"])
            central_line(model, X_39, X_494, 39, 494, incident=True)
            X_394 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A)', ID="X_394", classes=["center", "incident"])
            X_1504 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2) + 4*( area ))', ID="X_1504", classes=["center", "incident"])
            central_line(model, X_394, X_1504, 394, 1504, incident=True)
            return promote_point_to_top(model, X_493)


        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_493 on the given reference triangle."""
            model = create_model('X_493 = 1st VAN LAMOEN HOMOTHETIC CENTER')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00493(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-00493.json"))
            write_center_svg(
                model_acute,
                here / "x-00493.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X493¶

X₄₉₃¶