SHARYGIN 2008 Problem 19

(V.Protasov, 10-11) Given parallelogram $ABCD$ such that $AB = a$ , $AD = b$ . The first circle has its center at vertex $A$ and passes through $D$ , and the second circle has its center at $C$ and passes through $D$ . A circle with center $B$ meets the first circle at points $M_1$ , $N_1$ , and the second circle at points $M_2$ , $N_2$ . Determine the ratio $M_1N_1/M_2N_2$ .