JMO 2000 Problem 1

Consider the points $O(0,0)$ and $A(0,1/ 2)$ on the coordinate plane. Prove that there is no finite sequence of rational points $P_1,P_2,\ldots ,P_n$ in the plane such that $$OP_1=P_1P_2=\ldots =P_{n-1}P_n=P_nA=1$$