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X₆₈₅¶

TRILINEAR POLE OF LINE X₄X_98

X₆₈₅ (TRILINEAR POLE OF LINE X₄X_98) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_685 = TRILINEAR POLE OF LINE X_4X_98."""

        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_00685(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_685 = TRILINEAR POLE OF LINE X_4X_98 on reference triangle ABC."""
            X_684 = eval_trilinear_point(model, A, B, C, '(sec(B)*(sin(C))**(3) - sec(C)*(sin(B))**(3))', ID="X_684", classes=["center"])
            X_685 = isogonal_conjugate(model, A, B, C, X_684, ID="X_685", classes=["selected", "target"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_468 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cot(B) + cot(C) - 2*cot(A))', ID="X_468", classes=["center", "incident"])
            central_line(model, X_98, X_468, 98, 468, incident=True)
            X_287 = eval_trilinear_point(model, A, B, C, 'cot(A)*sec(A +  omega  )', ID="X_287", 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_287, X_297, 287, 297, incident=True)
            X_250 = eval_trilinear_point(model, A, B, C, '(sec(A))*(csc(B - C))**(2)', ID="X_250", classes=["center", "incident"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            central_line(model, X_250, X_523, 250, 523, incident=True)
            return promote_point_to_top(model, X_685)


        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_685 on the given reference triangle."""
            model = create_model('X_685 = TRILINEAR POLE OF LINE X_4X_98')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00685(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-00685.json"))
            write_center_svg(
                model_acute,
                here / "x-00685.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X685¶

X₆₈₅¶