Question 81
Let $AD$, $BE$ and $CF$ be the angle bisectors of triangle $ABC$. Assume
$$
\frac{1}{AE} + \frac{1}{AF} = \left( \frac{1}{\sqrt{AB}} + \frac{1}{\sqrt{AC}} \right)^2
$$
Prove that $AE + AF = BC$.
$$
\frac{1}{AE} + \frac{1}{AF} = \left( \frac{1}{\sqrt{AB}} + \frac{1}{\sqrt{AC}} \right)^2
$$
Prove that $AE + AF = BC$.