Problem:
On circle O, points C and D are on the same side of diameter AB,∠AOC=30∘, and ∠DOB=45∘. What is the ratio of the area of the smaller sector COD to the area of the circle? B
Answer Choices:
A. 92​
B. 41​
C. 185​
D. 247​
E. 103​
Solution:
The measure of ∠COD is 180∘−30∘−45∘=105∘. Therefore the ratio of the area of the sector to the area of the circle is 360105​=247​​.
The problems on this page are the property of the MAA's American Mathematics Competitions
