IMO Shortlist 2012 problem G5

  Avg: 3,0
  Avg: 8,0
Dodao/la: arhiva
3. studenoga 2013.
Let ABC be a triangle with \angle BCA=90^{\circ}, and let D be the foot of the altitude from C. Let X be a point in the interior of the segment CD. Let K be the point on the segment AX such that BK=BC. Similarly, let L be the point on the segment BX such that AL=AC. Let M be the point of intersection of AL and BK.

Show that MK=ML.

Proposed by Josef Tkadlec, Czech Republic
Izvor: Međunarodna matematička olimpijada, shortlist 2012