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

Difference between revisions of "Mock AIME 4 2006-2007 Problems/Problem 11"

 
m
Line 5: Line 5:
 
{{solution}}
 
{{solution}}
  
 +
 +
 +
----
 +
 +
*[[Mock AIME 4 2006-2007 Problems/Problem 12| Next Problem]]
 +
*[[Mock AIME 4 2006-2007 Problems/Problem 10| Previous Problem]]
 
*[[Mock AIME 4 2006-2007 Problems]]
 
*[[Mock AIME 4 2006-2007 Problems]]

Revision as of 10:49, 16 January 2007

Problem

Let $\triangle ABC$ be an equilateral triangle. Two points $D$ and $E$ are chosen on $\overline{AB}$ and $\overline{AC}$, respectively, such that $AD = CE$. Let $F$ be the intersection of $\overline{BE}$ and $\overline{CD}$. The area of $\triangle ABC$ is 13 and the area of $\triangle ACF$ is 3. If $\frac{CE}{EA}=\frac{p+\sqrt{q}}{r}$, where $p$, $q$, and $r$ are relatively prime positive integers, compute $p+q+r$.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.


Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_4_2006-2007_Problems/Problem_11&oldid=12186"