# Difference between revisions of "2006 AMC 12A Problems/Problem 13"

(added link to previous and next problem) |
(added category) |
||

Line 15: | Line 15: | ||

*[[2006 AMC 12A Problems/Problem 12|Previous Problem]] | *[[2006 AMC 12A Problems/Problem 12|Previous Problem]] | ||

*[[2006 AMC 12A Problems/Problem 14|Next Problem]] | *[[2006 AMC 12A Problems/Problem 14|Next Problem]] | ||

+ | |||

+ | [[Category:Introductory Geometry Problems]] |

## Revision as of 19:07, 5 November 2006

## Problem

The vertices of a right triangle are the centers of three mutually externally tangent circles, as shown. What is the sum of the areas of the three circles?

## Solution

Let the radius of the smallest circle be . We find that the radius of the largest circle is and the radius of the second largest circle is . Thus, . The radii of the other circles are and . The sum of their areas is