1st Junior Balkan 1997 Problem 4 A triangle has circumradius R and sides a, b, c with R(b+c) = a √(bc). Find its angles.
A = 90 o , B = 45 o , C = 45 o . Solution We have a = 2R sin A, so b+c = 2 sin A √(bc). But by AM/GM (b+c)/2 ≥ √(bc) with equality iff b = c. So we must have b = c and A = 90 o . Thanks to Suat Namli 1st Junior Balkan 1997 © John Scholes jscholes@kalva.demon.co.uk 3 February 2004 Last corrected/updated 3 Feb 04