2010 AMC 10B Problems/Problem 6
Problem
A circle is centered at , is a diameter and is a point on the circle with . What is the degree measure of ?
Solution 1
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 .
Solution 2 (Alcumus)
Note that . Because triangle is isosceles, .
Video Solution
~IceMatrix
See Also
2010 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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