IMO Shortlist 2010 problem G2


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23. lipnja 2013.
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Let P be a point interior to triangle ABC (with CA \neq CB). The lines AP, BP and CP meet again its circumcircle \Gamma at K, L, respectively M. The tangent line at C to \Gamma meets the line AB at S. Show that from SC = SP follows MK = ML.

Proposed by Marcin E. Kuczma, Poland
Izvor: Međunarodna matematička olimpijada, shortlist 2010