IrMO 1992 Problem 4

In a triangle $ABC$ , the points $A'$ , $B'$ and $C'$ on the sides opposite $A$ , $B$ and $C$ , respectively, are such that the lines $AA'$ , $BB'$ and $CC'$ are concurrent. Prove that the diameter of the circumscribed circle of the triangle $ABC$ equals the product $|AB'|\cdot |BC'|\cdot |CA'|$ divided by the area of the triangle $A'B'C'$ .