2011 IMO Shortlist G7

Let $A B C D E F$ be a convex hexagon all of whose sides are tangent to a circle $\omega$ with center $O$. Suppose that the circumcircle of triangle $A C E$ is concentric with $\omega$. Let $J$ be the foot of the perpendicular from $B$ to $C D$. Suppose that the perpendicular from $B$ to $D F$ intersects the line $E O$ at a point $K$. Let $L$ be the foot of the perpendicular from $K$ to $D E$. Prove that $D J=D L$.

设 $A B C D E F$ 为凸六边形，其所有边均与以 $O$ 为圆心的圆 $\omega$ 相切。假设三角形$A C E$的外接圆与$\omega$同心。令 $J$ 为从 $B$ 到 $C D$ 的垂线的底脚。假设从 $B$ 到 $D F$ 的垂线与线 $E O$ 相交于点 $K$。令$L$ 为从$K$ 到$D E$ 的垂线的底脚。证明 $D J=D L$。