Question

In a equilateral $△ABC,AD\perp BC$, prove that $A{D}^2=3B{D}^2$

Answer 1

In Equlateral $\Delta ABC$

$AD=\frac{\sqrt{3}}{2}a$

$BD=\frac{a}{2}$

$A{D}^2=3\frac{a^2}{4}3{\left(\frac{a}{2}\right)}^2=3B{D}^2$