2010 AMC 10B Problems/Problem 6
Contents
[hide]Problem
A circle is centered at ,
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
.
Video Solution
~IceMatrix
See Also
2010 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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All AMC 10 Problems and Solutions |
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