cho tam giac ABC, \(\widehat{A}\)=\(90^0\), duong cao AH=h, AB=b, BC=a, AC=b, E,F thu tu la hinh chieu cua H len AB va AC . Dat BE=m, CF=n
CMR
a, \(\frac{m}{n}=\frac{a^3}{b^3}\)
b,\(3h^2\)+\(m^2\)+\(n^2\)=\(a^2\)
c, \(amn=h^3\)
d, \(\sqrt[3]{m^2}+\sqrt[3]{n^2}=\sqrt[3]{a^2}\)
e, \(\frac{\sqrt{2}}{AA'}=\frac{1}{b}+\frac{1}{c}\)(AA' la phan giac goc trong \(\widehat{A}\))
f, \(\frac{1}{c}-\frac{1}{b}=\frac{\sqrt{2}}{AA'}\)