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4

Part of 2005 Bosnia and Herzegovina Team Selection Test

Problems(1)

Three points collinear

Source: Bosnia and Herzegovina Team Selection Test 2005 problem 1 day 2

10/6/2017
On the line which contains diameter PQPQ of circle k(S,r)k(S,r), point AA is chosen outside the circle such that tangent tt from point AA touches the circle in point TT. Tangents on circle kk in points PP and QQ are pp and qq, respectively. If PT∩q=NPT \cap q={N} and QT∩p=MQT \cap p={M}, prove that points AA, MM and NN are collinear.
geometrydiametertangentcollinear