Selection and Training Session

Given the parallelogram $ABCD$. The circle $S_1$ passes through the vertex $C$ and touches the sides $BA$ and $AD$ at points $P_1$ and $Q_1$ respectively. The circle $S_2$ passes through the vertex $B$ and touches the sides $DC$ and $AD$ at points $P_2$ and $Q_2$ respectively. Let $d_1,d_2$ be the distances from $C$ and $B$ to the lines $P_1{Q}_1$ and $P_2{Q}_2$ respectively. Find all possible values of the ratio $d_1:d_2$.