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X₆₅₈¶

TRILINEAR POLE OF LINE X₁X_7

X₆₅₈ (TRILINEAR POLE OF LINE X₁X_7) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_658 = TRILINEAR POLE OF LINE X_1X_7."""

        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,
            feuerbach_point_of,
            gergonne_point_of,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00658(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_658 = TRILINEAR POLE OF LINE X_1X_7 on reference triangle ABC."""
            X_657 = eval_trilinear_point(model, A, B, C, '(1 + cos(A))*(cos(B) - cos(C))', ID="X_657", classes=["center"])
            X_658 = isogonal_conjugate(model, A, B, C, X_657, ID="X_658", classes=["selected", "target"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            central_line(model, X_7, X_11, 7, 11, incident=True)
            X_88 = eval_trilinear_point(model, A, B, C, '1/(b + c - 2*a)', ID="X_88", classes=["center", "incident"])
            X_279 = eval_trilinear_point(model, A, B, C, 'csc(A)*(tan(A/2))**(2)', ID="X_279", classes=["center", "incident"])
            central_line(model, X_88, X_279, 88, 279, incident=True)
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            X_673 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) + c**(2) - a*(b + c))', ID="X_673", classes=["center", "incident"])
            central_line(model, X_57, X_673, 57, 673, incident=True)
            return promote_point_to_top(model, X_658)


        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_658 on the given reference triangle."""
            model = create_model('X_658 = TRILINEAR POLE OF LINE X_1X_7')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00658(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-00658.json"))
            write_center_svg(
                model_acute,
                here / "x-00658.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X658¶

X₆₅₈¶