← etc / Encyclopedia of Triangle Centers

X₅₈₆¶

2nd CONGRUENT SHRUNK INSQUARES POINT

For a discussion, see Floor van Lamoen, “Vierkanten in een driehoek: 5. Gekrompen ingeschreven vierkanten”

X₅₈₆ (2nd CONGRUENT SHRUNK INSQUARES POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_586 = 2nd CONGRUENT SHRUNK INSQUARES POINT."""

        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,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00586(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_586 = 2nd CONGRUENT SHRUNK INSQUARES POINT on reference triangle ABC."""
            X_586 = eval_trilinear_point(model, A, B, C, '((2*area*(1/b + 1/c - 1/a) + a - b - c)/a)', ID="X_586", classes=["selected", "target"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_192 = eval_trilinear_point(model, A, B, C, 'b*c*(c*a + a*b - b*c)', ID="X_192", classes=["center", "incident"])
            central_line(model, X_8, X_192, 8, 192, incident=True)
            return promote_point_to_top(model, X_586)


        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_586 on the given reference triangle."""
            model = create_model('X_586 = 2nd CONGRUENT SHRUNK INSQUARES POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00586(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-00586.json"))
            write_center_svg(
                model_acute,
                here / "x-00586.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X586¶

X₅₈₆¶