Problem:
Two circles intersect at points A and B. The minor arcs AB measure 30β on one circle and 60β on the other circle. What is the ratio of the area of the larger circle to the area of the smaller circle?
Answer Choices:
A. 2
B. 1+3β
C. 3
D. 2+3β
E. 4 Solution:
Let the larger and smaller circles have radii R and r, respectively. Then the length of chord AB can be expressed as both r and 2Rsin15β. The ratio of the areas of the circles is
Let the larger and smaller circles have radii R and r, and centers P and Q, respectively. Because β³QAB is equilateral, it follows that r=AB. The Law
of Cosines applied to β³PBA gives
