Hanoi Open Mathematics Competition 2011 Senior Question 10

Two angle bisectors \(BD\) and \(CE\) of triangle \(ABC\) intersect at \(O\). Suppose \(BD\cdot CE=2BO\cdot OC\). Let \(H\) be the point on \(BC\) such that \(OH\perp BC\). Prove \(AB\cdot AC=2HB\cdot HC\).