Question 39
The incircle of the triangle $ABC$ is centred at $I$, and touches the sides $\overline{BC}$, $\overline{CA}$ and $\overline{AB}$ in points $D, E$ and $F$, respectively. Let $k$ be a circle centred at $A$ passing through the point $E$. Let $K$ be the second intersection of the line $DE$ with $k$. The line parallel to $DF$ and passing through $I$ intersects the side $\overline{AB}$ at $P$. The point $L$ is the intersection of the line $CP$ with the circle $k$ such that the point $P$ is located between points $C$ and $L$. The point $O$ is the circumcentre of the triangle $DKL$.
Prove that the lines $AI$ and $OD$ are parallel. (Stipe Vidak)
Prove that the lines $AI$ and $OD$ are parallel. (Stipe Vidak)