2008 AMC 12B Problems/Problem 9
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Problem 9
Points 
and 
are on a circle of radius 
and 
. Point 
is the midpoint of the minor arc 
. What is the length of the line segment 
?
Solution
Trig Solution:
Let 
be the angle that subtends the arc AB. By the law of cosines,
The half-angle formula says that
, which is answer choice A.
Other Solution
Define D as the midpoint of AB, and R the center of the circle. R, C, and D are collinear, and since D is the midpoint of AB, 
, and so 
. Since 
, 
, and so 
See Also
| 2008 AMC 12B (Problems • Resources) | ||
| Preceded by Problem 8 | Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
