Difference between revisions of "2010 AMC 10B Problems/Problem 6"
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Revision as of 18:01, 28 June 2017
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
.
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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