AoPSWiki

Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.

Personal tools

Log in

Search

Toolbox

2006 Romanian NMO Problems/Grade 9/Problem 2

From AoPSWiki

Problem

Let $\displaystyle ABC$ and $\displaystyle DBC$ be isosceles triangles with the base $\displaystyle BC$ . We know that $\displaystyle \angle ABD = \frac{\pi}{2}$ . Let $\displaystyle M$ be the midpoint of $\displaystyle BC$ . The points $\displaystyle E,F,P$ are chosen such that $\displaystyle E \in (AB)$ , $\displaystyle P \in (MC)$ , $\displaystyle C \in (AF)$ , and $\displaystyle \angle BDE = \angle ADP = \angle CDF$ . Prove that $\displaystyle P$ is the midpoint of $\displaystyle EF$ and $\displaystyle DP \perp EF$ .

Solution

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

See also

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/2006_Romanian_NMO_Problems/Grade_9/Problem_2"

Categories: Problems with no solution | Olympiad Geometry Problems

Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.

© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us