1986 AHSME Problems/Problem 21
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Problem
In the configuration below, is measured in radians,
is the center of the circle,
and
are line segments and
is tangent to the circle at
.
A necessary and sufficient condition for the equality of the two shaded areas, given , is
Solution
Well, the shaded sector's area is basically (ratio of theta to total angle of circle) * (total area) = .
In addition, if you let , then
Then the area of that shaded thing on the left becomes
We want this to be equal to the sector area so
See also
1986 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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