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Part of 2004 Bosnia and Herzegovina Team Selection Test

Problems(1)

Bosnia and Herzegovina TST 2004 Day 1 Problem 1

Source: Bosnia and Herzegovina Team Selection Test 2004

9/17/2018
Circle kk with center OO is touched from inside by two circles in points SS and T,T, respectively. Let those two circles intersect at points MM and NN, such that NN is closer to line STST. Prove that OMOM and MNMN are perpendicular iff SS, NN and TT are collinear
circlecollineartouchinggeometry