Problem:
A circle is centered at O,AB is a diameter and C is a point on the circle with ∠COB=50∘. What is the degree measure of ∠CAB?
Answer Choices:
A. 20
B. 25
C. 45
D. 50
E. 65
Solution:
Note that ∠AOC=180∘−50∘=130∘. Because △AOC is isosceles, ∠CAB=21(180∘−130∘)=(B)25∘.
OR
By the Inscribed Angle Theorem, ∠CAB=21(∠COB)=21(50∘)=(B)25∘.
The problems on this page are the property of the MAA's American Mathematics Competitions
