2.2. On a circle, points $A, B, C, D, X$ are given, such that $\angle A X B = \angle B X C = \angle C X D$. The distances $A X = a$, $B X = b$, $C X = c$ are known. Find $D X$.
2.2. Answer: $X D=\left(a c+c^{2}-b^{2}\right) / b$. Let's place points $K, L$ on the extensions of segments $X A, X D$ respectively such that $A K=c, D L=b$. It is clear that $A B=B C=C D$ and $\angle X C B=\angle K A B$, so $\triangle K A B=\triangle X C B$ by two sides and the included angle, hence $K B=b$. Similarly, $C L=c$, and the isosceles triangles $X C L$ and $L B K$ are similar by the angle at the base, so $(X D+b): c=(a+c): b, X D=\left(a c+c^{2}-b^{2}\right) / b$.