IMO Shortlist 1993 problem G1


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2. travnja 2012.
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Let ABC be a triangle, and I its incenter. Consider a circle which lies inside the circumcircle of triangle ABC and touches it, and which also touches the sides CA and BC of triangle ABC at the points D and E, respectively. Show that the point I is the midpoint of the segment DE.
Izvor: Međunarodna matematička olimpijada, shortlist 1993