Difference between revisions of "2007 AMC 12B Problems/Problem 3"
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| − | The point O is the center of the circle circumscribed about triangle ABC, with <BOC = | + | ==Problem== |
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| + | The point <math>O</math> is the center of the circle circumscribed about triangle <math>ABC</math>, with <math>\angle BOC = 120^{\circ}</math> and <math>\angle AOB = 140^{\circ}</math>, as shown. What is the degree measure of <math>\angle ABC</math>? | ||
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| + | {{image}} | ||
A. 35 B. 40 C. 45 D. 50 E. 60 | A. 35 B. 40 C. 45 D. 50 E. 60 | ||
| − | { | + | ==Solution== |
| − | {{ | + | |
| + | <math>\angle AOC=360-140-120=100=2\angle ABC</math> | ||
| + | |||
| + | <math>\angle ABC=50 \Rightarrow \mathrm {D}</math> | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{AMC12 box|year=2007|ab=B|num-b=2|num-a=4}} | ||
Revision as of 09:07, 17 October 2007
Problem
The point 
is the center of the circle circumscribed about triangle 
, with 
and 
, as shown. What is the degree measure of 
?
An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.
A. 35 B. 40 C. 45 D. 50 E. 60
Solution
See Also
| 2007 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 2 |
Followed by Problem 4 |
| 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 | |
| All AMC 12 Problems and Solutions | |
