2005 Alabama ARML TST Problems/Problem 3
Problem
The difference between the areas of the circumcircle and incircle of an equilateral triangle is square units. Find the number of units in the length of a side of the triangle.
Solution
Let be the radius of the circumcircle, and let be the radius of the incircle. Then we have . But by similarity in the equilateral triangle , thus ; side length is equal to .