IrMO 2016 Problem 6

Triangle $ABC$ has sides $a = |BC| > b = |AC|$ . The points $K$ and $H$ on the segment $BC$ satisfy $|CH| = (a + b)/3$ and $|CK| = (a - b)/3$ . If $G$ is the centroid of triangle $ABC$ , prove that $\angle KGH = 90^o$ .