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X₆₅₅¶

TRILINEAR POLE OF LINE X₁X_5

X₆₅₅ (TRILINEAR POLE OF LINE X₁X_5) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_655 = TRILINEAR POLE OF LINE X_1X_5."""

        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_00655(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_655 = TRILINEAR POLE OF LINE X_1X_5 on reference triangle ABC."""
            X_654 = eval_trilinear_point(model, A, B, C, 'cos(A - B) - cos(C - A)', ID="X_654", classes=["center"])
            X_655 = isogonal_conjugate(model, A, B, C, X_654, ID="X_655", classes=["selected", "target"])
            X_59 = eval_trilinear_point(model, A, B, C, '1/(1 - cos(B - C))', ID="X_59", 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_59, X_523, 59, 523, incident=True)
            X_80 = eval_trilinear_point(model, A, B, C, '1/(1 - 2*cos(A))', ID="X_80", classes=["center", "incident"])
            X_516 = eval_trilinear_point(model, A, B, C, 'b*c*((a - b)*cot(C) + (a - c)*cot(B))', ID="X_516", classes=["center", "incident"])
            central_line(model, X_80, X_516, 80, 516, incident=True)
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center", "incident"])
            central_line(model, X_100, X_522, 100, 522, incident=True)
            return promote_point_to_top(model, X_655)


        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_655 on the given reference triangle."""
            model = create_model('X_655 = TRILINEAR POLE OF LINE X_1X_5')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00655(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-00655.json"))
            write_center_svg(
                model_acute,
                here / "x-00655.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X655¶

X₆₅₅¶