79. (YUG 3) Let $S$ be a unit circle and $K$ a subset of $S$ consisting of several closed arcs. Let $K$ satisfy the following properties:
(i) $K$ contains three points $A, B, C$, that are the vertices of an acuteangled triangle;
(ii) for every point $A$ that belongs to $K$ its diametrically opposite point $A^{\prime}$ and all points $B$ on an arc of length $1 / 9$ with center $A^{\prime}$ do not belong to $K$.
Prove that there are three points $E, F, G$ on $S$ that are vertices of an equilateral triangle and that do not belong to $K$.