1986 AHSME Problems/Problem 21
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 .
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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