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Show that the segments have equal lengths

Source: Finnish Mathematics Competition 2009, Final Round - P3

November 16, 2011
geometry unsolvedgeometry

Problem Statement

The circles Y0\mathcal{Y}_0 and Y1\mathcal{Y}_1 lies outside each other. Let O0O_0 be the center of Y0\mathcal{Y}_0 and O1O_1 be the center of Y1\mathcal{Y}_1. From O0O_0, draw the rays which are tangents to Y1\mathcal{Y}_1 and similarty from O1O_1, draw the rays which are tangents to Y0\mathcal{Y}_0. Let the intersection points of rays and circle Yi\mathcal{Y}_i be AiA_i and BiB_i. Show that the line segments A0B0A_0B_0 and A1B1A_1B_1 have equal lengths.
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