Đặt $\widehat{MAB}=\widehat{AID}=\alpha$ (so le trong)
Ta có:
$\frac{AD}{AI}=sin\alpha$⇔ $\frac{1}{AI}=$ $\frac{sin\alpha}{AD}=\frac{sin\alpha}{a}$ ⇔$\frac{1}{AI^2}=$ $\frac{sin^2\alpha}{a^2}$
$\frac{AB}{AM}=cos\alpha$⇔ $\frac{1}{AM}=$ $\frac{cos\alpha}{AB}=\frac{cos\alpha}{a}$ ⇔$\frac{1}{AM^2}=$ $\frac{cos^2\alpha}{a^2}$
Suy ra: $\frac{1}{AI^2}+\frac{1}{AM^2}=$\frac{sin^2\alpha+cos^2\alpha}{a^2}=$ $\frac{1}{a^2}$