AoPSWiki

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.

Personal tools

Search

Toolbox

2002 AMC 10B Problems/Problem 22

From AoPSWiki

Problem

Let $\triangle{XOY}$ be a right-triangle with $m\angle{XOY}=90^\circ$ . Let $M$ and $N$ be the midpoints of the legs $OX$ and $OY$ , respectively. Given $XN=19$ and $YM=22$ , find $XY$ .

Solution

Let $OM=MX=x$ and $ON=NY=y$ . By the Pythagorean Theorem, and We wish to find $\sqrt{4x^2+4y^2}$ . So, we add the two equations, multiply by $\frac{4}{5}$ , and take the squareroot to get $XY=26$

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/2002_AMC_10B_Problems/Problem_22"

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

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