BG-MO 1962 Problem 2

It is given a circle with center $O$ and radius $r$ . $AB$ and $MN$ are two diameters. The lines $MB$ and $NB$ are tangent to the circle at the points $M'$ and $N'$ and intersect at point $A$ . $M''$ and $N''$ are the midpoints of the segments $AM'$ and $AN'$ . Prove that:

(a) the points $M,N,N',M'$ are concyclic. (b) the heights of the triangle $M''N''B$ intersect in the midpoint of the radius $OA$ .