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Prove that A'B' = radius of C_1 - Iran NMO 2006 - Problem1

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September 23, 2010
geometry proposedgeometry

Problem Statement

Let C1,C2C_1,C_2 be two circles such that the center of C1C_1 is on the circumference of C2C_2. Let C1,C2C_1,C_2 intersect each other at points M,NM,N. Let A,BA,B be two points on the circumference of C1C_1 such that ABAB is the diameter of it. Let lines AM,BNAM,BN meet C2C_2 for the second time at A′,B′A',B', respectively. Prove that A′B′=r1A'B'=r_1 where r1r_1 is the radius of C1C_1.
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