2001 IMO Shortlist Problems/G2

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Problem

Consider an acute-angled triangle $ABC$ . Let $P$ be the foot of the altitude of triangle $ABC$ issuing from the vertex $A$ , and let $O$ be the circumcenter of triangle $ABC$ . Assume that $\angle C \geq \angle B + 30^{\circ}$ . Prove that $\angle A + \angle COP < 90^{\circ}$ .