In triangle ABC, let M be the midpoint of AB and N be on AC such that N is an altitude of ABC. If AB = AC = 13 and BC = \(18\), and AN and CM intersect at X, then what is AX?
This triangle is isoceles so AN and CM are medians
ANB forms aright triangle with NB = 9
AN = sqrt [ 13^2 - 9^2 ] = sqrt [ 88] = 2sqrt (22)
By the property of medians
AX = (2/3) AN = (2/3) * 2sqrt (22) = (4/3)sqrt (22)