← etc / Encyclopedia of Triangle Centers

X₁₆₆₀¶

1st GRINBERG MIDPOINTS PERSPECTOR

The lines AX_A, BX_B, CX_C concur in X₂₀.

X₁₆₆₀ (1st GRINBERG MIDPOINTS PERSPECTOR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1660 = 1st 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,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            midpoint,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01660(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1660 = 1st GRINBERG MIDPOINTS PERSPECTOR on reference triangle ABC."""
            X_394 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A)', ID="X_394", classes=["center"])
            X_1619 = point_from_barycentrics(model, A, B, C, 1.6442071, 2.1299263, -2.7741334, ID="X_1619", classes=["center"])
            X_1660 = midpoint(model, X_394, X_1619, ID="X_1660", classes=["selected", "target"], guide=False)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            central_line(model, X_6, X_25, 6, 25, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_156 = eval_barycentric_point(model, A, B, C, 'a**(2)*(a**(8) - 3*a**(6)*(b**(2) + c**(2)) + a**(4)*(3*b**(4) + 2*b**(2)*c**(2) + 3*c**(4)) - a**(2)*(b**(6) + c**(6)) + b**(2)*c**(2)*(b**(2) - c**(2))**(2))', ID="X_156", classes=["center", "incident"])
            central_line(model, X_30, X_156, 30, 156, incident=True)
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_1370 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(2)/(a**(2) - b**(2) + c**(2)) + c**(2)/(a**(2) + b**(2) - c**(2)) - a**(2)/(- a**(2) + b**(2) + c**(2))))', ID="X_1370", classes=["center", "incident"])
            central_line(model, X_110, X_1370, 110, 1370, incident=True)
            return promote_point_to_top(model, X_1660)


        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_1660 on the given reference triangle."""
            model = create_model('X_1660 = 1st GRINBERG MIDPOINTS PERSPECTOR')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01660(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-01660.json"))
            write_center_svg(
                model_acute,
                here / "x-01660.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1660¶

X₁₆₆₀¶