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Turkey Junior Olympiad 2008, Part II - P1

Source:

January 20, 2013
geometrygeometric transformationreflectionsymmetry

Problem Statement

Let ABCABC be a right triangle with m(C^)=90∘m(\widehat {C}) = 90^\circ, and DD be its incenter. Let NN be the intersection of the line ADAD and the side CBCB. If ∣CA∣+∣AD∣=∣CB∣|CA|+|AD|=|CB|, and ∣CN∣=2|CN|=2, then what is ∣NB∣|NB|?
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