Difference between revisions of "2010 AMC 10B Problems/Problem 6"
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Revision as of 12:01, 4 July 2013
Problem
A circle is centered at , $\overbar{AB}$ (Error compiling LaTeX. ! Undefined control sequence.) is a diameter and is a point on the circle with . What is the degree measure of ?
Solution
Assuming we do not already know an inscribed angle is always half of its central angle, we will try a different approach. Since is the center, and are radii and they are congruent. Thus, is an isosceles triangle. Also, note that and are supplementary, then . Since is isosceles, then . They also sum to , so each angle is .
See Also
2010 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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 10 Problems and Solutions |
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