IMO Shortlist 1969 problem 47


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2. travnja 2012.
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C is a point on the semicircle diameter AB, between A and B. D is the foot of the perpendicular from C to AB. The circle K_1 is the incircle of ABC, the circle K_2 touches CD,DA and the semicircle, the circle K_3 touches CD,DB and the semicircle. Prove that K_1,K_2 and K_3 have another common tangent apart from AB.
Izvor: Međunarodna matematička olimpijada, shortlist 1969