IMO Shortlist 2010 problem G2

  Avg: 2.5
  Avg: 6.0
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
Source: Međunarodna matematička olimpijada, shortlist 2010