Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2001 IMO Shortlist Problems/G2

Revision as of 12:27, 28 January 2022 by Hastapasta (talk | contribs) (→‎Solution)

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

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it. See 2001 IMO 1 page.

Resources

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2001_IMO_Shortlist_Problems/G2&oldid=170496"