+6 Let ABC be an acute-angled triangle and let ha, hb, hc be the lengths of its altitudes, while r and R denote the inradius and the circumradius of ABC, respectively. Prove that
a) AH + BH + CH = 2R(cos A + cos B + cos C); (Hint: In order to compute AH, show that AE = c cos A, HE = AE · cot C = 2R cos A cos C, where E is the foot of the altitude ha from A).
b) ha + hb + hc ≤ 3(r + R) (Hint: Use Erdos-Mordell inequality for the point H)
