Question 87
The circle inscribed in $\triangle A B C$ has center $I$ and touches the side $B C$ at the point $D$. Points $P$ and $Q$ are chosen on the segments $B I$ and $C I$, respectively, such that $\varangle B A C=2 \varangle P A Q$. Prove: $\varangle P D Q=90^\circ$.
(Dušan Đukić)
(Dušan Đukić)