IL-GILLIS 2011 Problem 4

Let $\alpha_1,\alpha_2,\alpha_3$ be three congruent circles that are tangent to each other. A third circle $\beta$ is tangent to them at points $A_1,A_2,A_3$ respectively. Let $P$ be a point on $\beta$ which is different from $A_1,A_2,A_3$ . For $i=1,2,3$ , let $B_i$ be the second intersection point of the line $PA_i$ with circle $\alpha_i$ . Prove that $\Delta B_1B_2B_3$ is equilateral.