International Mathematical Olympiad 2001 — Official contest Question 1

Let $ABC$ be an acute-angled triangle with $O$ as its circumcenter. Let $P$ on line $BC$ be the foot of the altitude from $A$. Assume that $\angle BCA \ge \angle ABC + 30^\circ$. Prove that $\angle CAB + \angle COP \lt 90^\circ$.