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X₁₉₈₇¶

1st LEMOINE ANTIPARALLELS POINT

X₁₉₈₇ is discussed in Lemoine’s paper cited at X₁₉. Contributed by Darij Grinberg.

X₁₉₈₇ (1st LEMOINE ANTIPARALLELS POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1987 = 1st 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_trilinear_point,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01987(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1987 = 1st LEMOINE ANTIPARALLELS POINT on reference triangle ABC."""
            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"])
            X_1987 = isogonal_conjugate(model, A, B, C, X_401, ID="X_1987", classes=["selected", "target"])
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            central_line(model, X_54, X_112, 54, 112, incident=True)
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center", "incident"])
            X_248 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*sec(A +  omega  )', ID="X_248", classes=["center", "incident"])
            central_line(model, X_237, X_248, 237, 248, incident=True)
            X_290 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)*sec(A +  omega  )', ID="X_290", classes=["center", "incident"])
            X_297 = eval_trilinear_point(model, A, B, C, 'csc(2*A)*cos(A +  omega  )', ID="X_297", classes=["center", "incident"])
            central_line(model, X_290, X_297, 290, 297, incident=True)
            return promote_point_to_top(model, X_1987)


        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_1987 on the given reference triangle."""
            model = create_model('X_1987 = 1st LEMOINE ANTIPARALLELS POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01987(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-01987.json"))
            write_center_svg(
                model_acute,
                here / "x-01987.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1987¶

X₁₉₈₇¶