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cyclic and circumscribed

Source: Tournament of Towns,Spring 2002, Junior O Level, P4

May 13, 2014
geometry proposedgeometry

Problem Statement

Quadrilateral ABCDABCD is circumscribed about a circle Γ\Gamma and K,L,M,NK,L,M,N are points of tangency of sides AB,BC,CD,DAAB,BC,CD,DA with Γ\Gamma respectively. Let S≡KM∩LNS\equiv KM\cap LN. If quadrilateral SKBLSKBL is cyclic then show that SNDMSNDM is also cyclic.
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