MathDB

8

Part of 2002 IMO Shortlist

Problems(1)

IMO ShortList 2002, geometry problem 8

Source: IMO ShortList 2002, geometry problem 8

9/28/2004
Let two circles S1S_{1} and S2S_{2} meet at the points AA and BB. A line through AA meets S1S_{1} again at CC and S2S_{2} again at DD. Let MM, NN, KK be three points on the line segments CDCD, BCBC, BDBD respectively, with MNMN parallel to BDBD and MKMK parallel to BCBC. Let EE and FF be points on those arcs BCBC of S1S_{1} and BDBD of S2S_{2} respectively that do not contain AA. Given that ENEN is perpendicular to BCBC and FKFK is perpendicular to BDBD prove that ∠EMF=90∘\angle EMF=90^{\circ}.
geometrycirclesright angleIMO Shortlist