PROBLEM 4. Let $A B C$ be a right-angled triangle at $A$ and $[B D,[C E$ its angle bisectors $(D \in A C$, $E \in A B)$. Denote by $I$ the intersection of lines $B D$ and $C E$ and by $F$, respectively $G$, the projections of points $D$ and $E$ onto line $B C$. Determine the measure of angle $F I G$.[^0]

## NATIONAL MATHEMATICS OLYMPIAD Local stage - 14.02. 2015 GRADING KEY - Grade 7