Difference between revisions of "2010 AMC 10B Problems/Problem 6"
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==Problem== | ==Problem== | ||
− | A circle is centered at <math>O</math>, <math>\ | + | A circle is centered at <math>O</math>, <math>\overline{AB}</math> is a diameter and <math>C</math> is a point on the circle with <math>\angle COB = 50^\circ</math>. What is the degree measure of <math>\angle CAB</math>? |
<math>\textbf{(A)}\ 20 \qquad \textbf{(B)}\ 25 \qquad \textbf{(C)}\ 45 \qquad \textbf{(D)}\ 50 \qquad \textbf{(E)}\ 65</math> | <math>\textbf{(A)}\ 20 \qquad \textbf{(B)}\ 25 \qquad \textbf{(C)}\ 45 \qquad \textbf{(D)}\ 50 \qquad \textbf{(E)}\ 65</math> |
Revision as of 20:45, 13 March 2015
Contents
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
An inscribed angle is always half its central angle, so therefore, half of 50 is 25, or B. We can see this when we graph the problem.
(Solution by Flamedragon)
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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