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
.