Around an acute triangle $B C D$, a circle is described, and a tangent $C A$ is drawn to it at point $C$.

Another circle touches the line $B D$ at point $D$, passes through point $C$, and intersects the line $C A$ again at point $A$. It is known that $A D=a, B C=b, B D=c$. Find $A C$.
Triangles $B C D$ and $C D A$ are similar.

## Answer

$c \sqrt{\frac{a}{b}}$.

Problem