Problem: A circle with radius r is contained within the region bounded by a circle with radius R. The area bounded by the larger circle is ba​ times the area of the region outside the smaller circle and inside the larger circle. Then R : r equals:
Answer Choices:
A. a​:b​
B. a​:a−b​
C. b​:a−b​
D. a:a−b​
E. b:a−b​
Solution:
πR2=ba​(πR2−πr2)∴r2ba​=R2(ba​−1) so that r2R2​=a/b−1a/b​=a−ba​ and, hence, R:r=a​:a−b​.