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X₁₉₈₈¶

2nd LEMOINE ANTIPARALLELS POINT

X₁₉₈₈ is discussed in Lemoine’s paper cited at X₁₉. Contributed by Darij Grinberg.

X₁₉₈₈ (2nd LEMOINE ANTIPARALLELS POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1988 = 2nd LEMOINE ANTIPARALLELS 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_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01988(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1988 = 2nd LEMOINE ANTIPARALLELS POINT on reference triangle ABC."""
            X_1988 = eval_trilinear_point(model, A, B, C, '((sin(A))/(csc(2*B) + csc(2*C) - csc(2*A)))', ID="X_1988", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_436 = eval_barycentric_point(model, A, B, C, '(a**(2) + b**(2) - c**(2)) * (a**(2) - b**(2) + c**(2)) * (a**(8) - 2*a**(6)*b**(2) + a**(4)*b**(4) - 2*a**(6)*c**(2) + 3*a**(4)*b**(2)*c**(2) - b**(6)*c**(2) + a**(4)*c**(4) + 2*b**(4)*c**(4) - b**(2)*c**(6))', ID="X_436", classes=["center", "incident"])
            central_line(model, X_6, X_436, 6, 436, incident=True)
            X_394 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A)', ID="X_394", classes=["center", "incident"])
            X_401 = eval_trilinear_point(model, A, B, C, '(sin(2*B)*sin(2*C) - (sin(2*A))**(2))*(csc(A))', ID="X_401", classes=["center", "incident"])
            central_line(model, X_394, X_401, 394, 401, incident=True)
            X_184 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A)', ID="X_184", classes=["center", "incident"])
            X_1968 = eval_trilinear_point(model, A, B, C, 'a*((tan(A))**(2) + tan(B)*tan(C))', ID="X_1968", classes=["center", "incident"])
            central_line(model, X_184, X_1968, 184, 1968, incident=True)
            return promote_point_to_top(model, X_1988)


        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_1988 on the given reference triangle."""
            model = create_model('X_1988 = 2nd LEMOINE ANTIPARALLELS POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01988(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-01988.json"))
            write_center_svg(
                model_acute,
                here / "x-01988.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1988¶

X₁₉₈₈¶