CMO 1988 Problem 2

Given two circles $C_1,C_2$ with common center, the radius of $C_2$ is twice the radius of $C_1$ . Quadrilateral $A_1A_2A_3A_4$ is inscribed in $C_1$ . The extension of $A_4A_1$ meets $C_2$ at $B_1$ ; the extension of $A_1A_2$ meets $C_2$ at $B_2$ ; the extension of $A_2A_3$ meets $C_2$ at $B_3$ ; the extension of $A_3A_4$ meets $C_2$ at $B_4$ . Prove that $P(B_1B_2B_3B_4)\ge 2P(A_1A_2A_3A_4)$ , and in what case the equality holds? ( $P(X)$ denotes the perimeter of quadrilateral $X$ )