MathDB

1

Part of 2008 Turkey Junior National Olympiad

Problems(1)

Turkey Junior Olympiad 2008, Part II - P1

Source:

1/20/2013
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|?
geometrygeometric transformationreflectionsymmetry