← etc / Encyclopedia of Triangle Centers

X₁₆₆₁¶

2nd GRINBERG MIDPOINTS PERSPECTOR

X₁₆₆₁ is described at X₁₆₆₀.

X₁₆₆₁ (2nd GRINBERG MIDPOINTS PERSPECTOR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1661 = 2nd GRINBERG MIDPOINTS PERSPECTOR."""

        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,
            ceva_conjugate,
            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_01661(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1661 = 2nd GRINBERG MIDPOINTS PERSPECTOR on reference triangle ABC."""
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_1661 = ceva_conjugate(model, A, B, C, X_20, X_6, ID="X_1661", classes=["selected", "target"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_393 = eval_trilinear_point(model, A, B, C, 'b*c*(tan(A))**(2)', ID="X_393", classes=["center", "incident"])
            central_line(model, X_25, X_393, 25, 393, incident=True)
            X_154 = eval_trilinear_point(model, A, B, C, '(cos(A) - cos(B)*cos(C))*a**(2)', ID="X_154", classes=["center", "incident"])
            X_577 = eval_trilinear_point(model, A, B, C, 'sin(A)*(cos(A))**(2)', ID="X_577", classes=["center", "incident"])
            central_line(model, X_154, X_577, 154, 577, incident=True)
            X_1619 = point_from_barycentrics(model, A, B, C, 1.6442071, 2.1299263, -2.7741334, ID="X_1619", classes=["center", "incident"])
            X_1624 = point_from_barycentrics(model, A, B, C, 0.18909568, -0.24246678, 1.0533711, ID="X_1624", classes=["center", "incident"])
            central_line(model, X_1619, X_1624, 1619, 1624, incident=True)
            return promote_point_to_top(model, X_1661)


        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_1661 on the given reference triangle."""
            model = create_model('X_1661 = 2nd GRINBERG MIDPOINTS PERSPECTOR')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01661(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-01661.json"))
            write_center_svg(
                model_acute,
                here / "x-01661.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1661¶

X₁₆₆₁¶