## 2014 Singapore MO (Open Rd 1) Problem 5

2014 SMO (Open-Rd1) 5. The figure below (not drawn to scale) shows a triangle $ABC$ with $BC = 8$ cm, $BA = 4$ cm and $AC = 2\sqrt{31}$ cm. The point $M$ is the midpoint of $AC$. Find the length of $BM$ in centimetres.