Subject :IMO Class : Class 9

*ABCD* is a parallelogram. Two lines *l* and *m* are parallel to *AD*. Line *l* meets *AB* and *CD* at *P* and S respectively. Line* m* meets *AB* and *CD* at *Q* and *R* respectively. *X* is any point on *CD* between *R* and *S*. If ar (∆*DPX*) + ar(∆*CQX*) = *k *ar(*ABCD*), find *k*.

A

B

C

D