+389
A rectangle contains two circles of radius 6 that are each tangent to the rectangle in exactly 3 points. If the distance between the centers of the circles is 10, what is the area of the rectangle?
Solution:
Three sides of the rectangle must be tangent to each circle. In particular, since a pair of parallel sides must both be tangent to a particular circle, the distance between these sides must be the diameter, or 12. The height of the rectangle is 12. Since the circles are distinct, each of the other two sides of the rectangle is tangent to one of the circles.
The width of the rectangle can be dissected into the length of the radius of the left circle, the distance between the centers, and then the length of the radius of the right circle. Therefore the width is 6 + 10 + 6= 22
The area is 22*12 = 264
