# Mathematics and Youth Magazine Problems 2009

### Issue 379

1. Find all pairs of integers $a$, $b$ such that $$a^{2}+a b+b^{2}=a^{2} b^{2}$$
2. Let $ABC$ be an isosceles triangle (at vertex $A$) such that $\widehat{B A C} \geq 90^\circ$. Choose a point $M$ on $A C$, and let $A H$ and $C K$ be the altitudes from $A$ and $C$ onto $B M$ respectively $(H, K$ are the feet of these altitudes) such that $B H=H K+K C$. Find the angle $B A C$.