Difference between revisions of "2017 AMC 8 Problems/Problem 25"
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Revision as of 15:00, 22 November 2017
Problem 25
In the figure shown, and
are line segments each of length 2, and
. Arcs
and
are each one-sixth of a circle with radius 2. What is the area of the region shown?
Solution
Let the centers of the circles containing arcs and
be
and
, respectively. Extend
and
to
and
. The area of the figure is equal to the area of equilateral triangle
minus the combined area of the
sectors of the circles. The area of
is
The combined area of the
sectors is
Our final answer is then
~nukelauncher
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Problem | |
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 AJHSME/AMC 8 Problems and Solutions |
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