RIOPLATENSE 1992 Problem 3

Let $D$ be the center of the circumcircle of the acute triangle $ABC$ . If the circumcircle of triangle $ADB$ intersects $AC$ (or its extension) at $M$ and also $BC$ (or its extension) at $N$ , show that the radii of the circumcircles of $\triangle ADB$ and $\triangle MNC$ are equal.