IMO 2000

For discussing Olympiad level Geometry Problems
shehab ahmed
Posts: 66
Joined: Tue Mar 20, 2012 12:52 am

IMO 2000

Unread post by shehab ahmed » Wed May 30, 2012 12:18 pm

Two circles x and y intersect at M and N.Let l be the common tangent to x and y such that M is closer to l than N is.Let l touch x at A and y at B.Let the line through M parallel to l meet the circle x again at C and the circle y again at D.Lines CA and DB meet at E,lines AN and CD meet at P,lines BN and CD meet at Q.Show that EP=EQ

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FahimFerdous
Posts: 176
Joined: Thu Dec 09, 2010 12:50 am
Location: Mymensingh, Bangladesh

Re: IMO 2000

Unread post by FahimFerdous » Wed May 30, 2012 1:17 pm

Relatively easy as an IMO problem. You just have to prove that EM is perpendicular to CD and a few other little things.
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