**C. 1351.** Trapezium \(\displaystyle ABCD\) has an inscribed circle that touches the sides \(\displaystyle AB\), \(\displaystyle BC\), \(\displaystyle CD\) and \(\displaystyle DA\) at points \(\displaystyle E\), \(\displaystyle F\), \(\displaystyle G\) and \(\displaystyle H\), respectively. The interior angle at vertex \(\displaystyle B\) is \(\displaystyle 60^\circ\). Let \(\displaystyle I\) denote the intersection of lines \(\displaystyle AD\) and \(\displaystyle FG\), and let \(\displaystyle K\) denote the midpoint of \(\displaystyle FH\). Prove that if \(\displaystyle HE\) is parallel to \(\displaystyle BC\) then \(\displaystyle IK\) is also parallel to them.

(5 points)

This problem is for grade 1 - 10 students only.

**Deadline expired on 10 May 2016.**