In a triangle $ABC$, let $D,E, F$ be interior points of sides $BC,CA,AB$ respectively. Let $AD,BE,CF$ meet the circumcircle of triangle $ABC$ in $K, L,M$ respectively. Prove that $\frac{AD}{DK} + \frac{BE}{EL} + \frac{CF}{FM} \ge 9$. When does the equality hold?