a) Ap dung he thuc luong trong tam giac vuong ta co
$\dfrac{1}{AH^2} = \dfrac{1}{AB^2} + \dfrac{1}{AC^2}$
<-> $AH^2 = 5184$ <-> AH = 72 (cm)
THeo Pytago ta co
$BC^2 = AB^2 + AC^2$ <-> $BC^2 = 150$ (cm)
Theo He thuc luong trong tam giac vuong ta co
$AB^2 = BH.BC$ <-> $90^2 = BH.150$ <-> BH = 54 (cm)
CH = BC-BH = 150-54 = 96 (cm)
b) Do tam giac vuong nen duong trung tuyen cua goc vuong bang mot nua canh huyen.
Vay AI = BC/2 = 75 (cm)
c) Ap dung he thuc luong trong tam giac vuong AHB ta co
$$AM.AB = AH^2$$
Tuong tu trong tam giac vuong AHC ta cx co $AN.AC = AH^2$
Vay AM.AB = AN.AC ($=AH^2$)