2011 AMC 10A Problems/Problem 18
Problem 18
Circles and each have radius 1. Circles and share one point of tangency. Circle has a point of tangency with the midpoint of . What is the area inside Circle but outside circle and circle ?
Solution
Draw a rectangle with vertices at the centers of and and the intersection of and . Then, we can compute the shades area as the area of half of plus the area of the rectangle minus the area of the two sectors created by and . This is .