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/G6

Revision as of 17:49, 20 August 2008 by Minsoens (talk | contribs) (New page: == Problem == Let <math>ABC</math> be a triangle and <math>P</math> an exterior point in the plane of the triangle. Suppose the lines <math>AP</math>, <math>BP</math>, <math>CP</math> meet...)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $ABC$ be a triangle and $P$ an exterior point in the plane of the triangle. Suppose the lines $AP$, $BP$, $CP$ meet the sides $BC$, $CA$, $AB$ (or extensions thereof) in $D$, $E$, $F$, respectively. Suppose further that the areas of triangles $PBD$, $PCE$, $PAF$ are all equal. Prove that each of these areas is equal to the area of triangle $ABC$ itself.

Solution

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

Resources

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2001_IMO_Shortlist_Problems/G6&oldid=27515"