Problem:
Three circles pass through the origin. The center of the first circle lies in the first quadrant, the center of the second lies in the second quadrant, the center of the third lies in the third quadrant. If is a point interior to the three circles, then
Pick one
Solution:
The answer is (A). Observe that if a circle passes through the origin and has its center in a quadrant, then no interior point lies in the opposite quadrant. In particular, if is interior to the three circles, then it must lie in the second quadrant, since the three centers lie in the first, second and third quadrants. Indeed such a point can exist, as shown in the accompanying drawing.
