1994 AHSME Problems/Problem 29
Contents
[hide]Problem
Points and on a circle of radius are situated so that , and the length of minor arc is . If angles are measured in radians, then
Solution 1
First note that arc length equals , where is the central angle in radians. Call the center of the circle . Then radian because the minor arc has length . Since is isosceles, . We use the Law of Cosines to find that Using half-angle formulas, we have that this ratio simplifies to
Solution 2
Let the center of this circle be , , the radius of be .
By the definition of radian,
,
See Also
1994 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 28 |
Followed by Problem 30 | |
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