1960 AMC 12 Problem 7

Question

Circle I passes through the center of, and is tangent to, circle II. The area of circle I is

4

square inches. Then the area of circle II, in square inches, is:

8

8\sqrt2

8\sqrt\pi

16

16\sqrt2

Draw the line through the two centers and the tangency point

The radius of circle II is twice the radius of circle I

Because circle I passes through the center of circle II, the distance between the centers equals the radius

r

of circle I. Internal tangency also makes that distance

R-r,

where

R

is the radius of circle II. Thus

R=2r,

and the area is multiplied by

2^2=4.

It is therefore

4\cdot4=16.

Thus, the correct answer is D.

Problem 7 in other years