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Tangent circles

Source: May Olympiad (Olimpiada de Mayo) 2000

February 27, 2018
geometry

Problem Statement

Let SS be a circle with radius 22, let S1S_1 be a circle,with radius 11 and tangent, internally to SS in BB and let S2S_2 be a circle, with radius 11 and tangent to S1S_1 in AA, but S2S_2 isn't tangent to SS. If KK is the point of intersection of the line ABAB and the circle SS, prove that KK is in the circle S2S_2.
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