AUSTRIAN-POLISH 1993 Problem 9

Point $P$ is taken on the extension of side $AB$ of an equilateral triangle $ABC$ so that $A$ is between $B$ and $P$ . Denote by $a$ the side length of triangle $ABC$ , by $r_1$ the inradius of triangle $PAC$ , and by $r_2$ the exradius of triangle $PBC$ opposite $P$ . Find the sum $r_1+r_2$ as a function in $a$ .