2001 IMO Shortlist Problems/G2

Revision as of 15:06, 17 March 2022 by Hastapasta (talk | contribs) (Solution)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)


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 $\angle A + \angle COP < 90^{\circ}$.


See 2001 IMO 1 page. https://artofproblemsolving.com/wiki/index.php/2001_IMO_Problems/Problem_1