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X₆₈₇¶

TRILINEAR POLE OF LINE X₄X_110

X₆₈₇ (TRILINEAR POLE OF LINE X₄X_110) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_687 = TRILINEAR POLE OF LINE X_4X_110."""

        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_00687(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_687 = TRILINEAR POLE OF LINE X_4X_110 on reference triangle ABC."""
            X_686 = eval_trilinear_point(model, A, B, C, '(sec(B)*csc(A - B) + sec(C)*csc(A - C))', ID="X_686", classes=["center"])
            X_687 = isogonal_conjugate(model, A, B, C, X_686, ID="X_687", classes=["selected", "target"])
            X_107 = eval_trilinear_point(model, A, B, C, '1/(cos(A)*(sin(2*B) - sin(2*C)))', ID="X_107", classes=["center", "incident"])
            X_250 = eval_trilinear_point(model, A, B, C, '(sec(A))*(csc(B - C))**(2)', ID="X_250", classes=["center", "incident"])
            central_line(model, X_107, X_250, 107, 250, incident=True)
            X_249 = eval_trilinear_point(model, A, B, C, '(csc(A))*(csc(B - C))**(2)', ID="X_249", classes=["center", "incident"])
            X_648 = eval_trilinear_point(model, A, B, C, '1/(a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2)))', ID="X_648", classes=["center", "incident"])
            central_line(model, X_249, X_648, 249, 648, incident=True)
            return promote_point_to_top(model, X_687)


        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_687 on the given reference triangle."""
            model = create_model('X_687 = TRILINEAR POLE OF LINE X_4X_110')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00687(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-00687.json"))
            write_center_svg(
                model_acute,
                here / "x-00687.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X687¶

X₆₈₇¶