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X₆₅₁¶

TRILINEAR POLE OF LINE X₁X_3

X₆₅₁ (TRILINEAR POLE OF LINE X₁X_3) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_651 = TRILINEAR POLE OF LINE X_1X_3."""

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


        def construct_x_00651(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_651 = TRILINEAR POLE OF LINE X_1X_3 on reference triangle ABC."""
            X_650 = eval_trilinear_point(model, A, B, C, 'cos(B) - cos(C)', ID="X_650", classes=["center"])
            X_651 = isogonal_conjugate(model, A, B, C, X_650, ID="X_651", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_6, X_7, 6, 7, incident=True)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_77 = eval_trilinear_point(model, A, B, C, '1/(1 + sec(A))', ID="X_77", classes=["center", "incident"])
            central_line(model, X_9, X_77, 9, 77, incident=True)
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            X_73 = eval_trilinear_point(model, A, B, C, 'sec(B) + sec(C)', ID="X_73", classes=["center", "incident"])
            central_line(model, X_21, X_73, 21, 73, incident=True)
            return promote_point_to_top(model, X_651)


        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_651 on the given reference triangle."""
            model = create_model('X_651 = TRILINEAR POLE OF LINE X_1X_3')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00651(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-00651.json"))
            write_center_svg(
                model_acute,
                here / "x-00651.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X651¶

X₆₅₁¶