Ta có:
$S_{ABC} =\dfrac12AB.AC =\dfrac12BC.AH$
$\Leftrightarrow AB.AC = BC.AH$
$\Rightarrow AB^2.AC^2 = BC^2.AH^2$
$\Leftrightarrow \dfrac{1}{AH^2}=\dfrac{BC^2}{AB^2.AC^2}$
$\Leftrightarrow \dfrac{1}{AH^2}=\dfrac{AB^2 + AC^2}{AB^2.AC^2}$
$\Leftrightarrow \dfrac{1}{AH^2}=\dfrac{1}{AB^2} +\dfrac{1}{AC^2}$