**B. 4539.** The centroid of a triangle *ABC* is *S*, and its circumcentre is *K*. The centres of the circumscribed circles of the triangles *BCS*, *CAS* and *ABS* are *P*, *Q *and *R*. Prove that *K* is the centroid of triangle *PQR*.

(Suggested by *Zs. Sárosdi,* Veresegyház)

(5 points)