Let $C_1,C_2,..., C_n$ , $(n\ge 3)$ be circles having a common point $M$. Three straight lines passing through $M$ intersect again the circles in $A_1, A_2,..., A_n$ ; $B_1,B_2,..., B_n$ and $X_1,X_2,..., X_n$ respectively. Prove that if $$A_1A_2 =A_2A_3 =...=A_{n-1}A_n$$and $$B_1B_2 =B_2B_3 =...=B_{n-1}B_n$$then $$X_1X_2 =X_2X_3 =...=X_{n-1}X_n.$$