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

2009 IMO Problems/Problem 4

Revision as of 05:27, 23 July 2009 by Bugi (talk | contribs) (Created page with '== Problem == Let <math>ABC</math> be a triangle with <math>AB=AC</math>. The angle bisectors of <math>\angle CAB</math> and <math>\angle BAC</math> meet the sides <math>BC</mat…')
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $ABC$ be a triangle with $AB=AC$. The angle bisectors of $\angle CAB$ and $\angle BAC$ meet the sides $BC$ and $CA$ at $D$ and $E$, respectively. Let $K$ be the incentre of triangle $ADC$. Suppose that $\angle BEK=45^\circ$. Find all possible values of $\angle CAB$.

Authors: Jan Vonk and Peter Vandendriessche, Belgium, and Hojoo Lee, South Korea

--Bugi 10:27, 23 July 2009 (UTC)Bugi

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2009_IMO_Problems/Problem_4&oldid=32496"