SHARYGIN 2007 Problem 19

Into an angle $A$ of size $a$ , a circle is inscribed tangent to its sides at points $B$ and $C$ . A line tangent to this circle at a point M meets the segments $AB$ and $AC$ at points $P$ and $Q$ respectively. What is the minimum $a$ such that the inequality $S_{PAQ}<S_{BMC}$ is possible?