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 baβ times the area of the region outside the smaller circle and inside the larger circle. Then R : r equals:
Answer Choices:
A. aβ:bβ
B. aβ:aβbβ
C. bβ:aβbβ
D. a:aβbβ
E. b:aβbβ
Solution:
ΟR2=baβ(ΟR2βΟr2)β΄r2baβ=R2(baββ1) so that r2R2β=a/bβ1a/bβ=aβbaβ and, hence, R:r=aβ:aβbβ.