Giả sử: $\dfrac{1}{AB^2}+\dfrac{1}{AC^2}=\dfrac{1}{AH^2}$
Ta có: $AB.AC=BC.AH$ (hệ thức lượng)
$⇒AB^2.AC^2=BC^2.AH^2$
$\dfrac{AC^2}{AB^2.AC^2}+\dfrac{AB^2}{AC^2.AB^2}=\dfrac{1}{AH^2}$
$⇒\dfrac{AC^2+AB^2}{AB^2.AC^2}=\dfrac{1}{AH^2}$
$⇒\dfrac{BC^2}{BC^2.AH^2}=\dfrac{1}{AH^2}$
$⇒\dfrac{1}{AH^2}=\dfrac{1}{AH^2}$ (luôn đúng)
$⇒ĐPCM$
