Xét \(\Delta OBC\)có: OH _|_ BC
=> \(\frac{1}{OH^2}=\frac{1}{OB^2}+\frac{1}{OC^2}\)hay \(\frac{1}{h^2}=\frac{1}{OB^2}+\frac{1}{OC^2}\)(*)
\(AC=m\Rightarrow OC=\frac{1}{2}AC=\frac{1}{2}m\)
\(BD=n\Rightarrow OB=\frac{1}{2}BD=\frac{1}{2}n\)
Thay vào pt (*) => \(\frac{1}{h^2}=\frac{1}{\left(\frac{1}{2}m\right)^2}+\frac{1}{\left(\frac{1}{2}n\right)^2}=\frac{4}{m^2}+\frac{4}{n^2}\)
\(\Rightarrow\frac{1}{4h^2}=\frac{1}{m^2}+\frac{1}{n^2}\)