Mock AIME 4 2006-2007 Problems/Problem 4
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Problem
Points 
, 
, and 
are on the circumference of a unit circle so that the measure of 
is 
, the measure of 
is 
, and the measure of 
is 
. The area of the triangular shape bounded by and line segments 
and 
can be written in the form 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
Let the center of the circle be 
. The area of the desired region is easily seen to be that of sector 
plus the area of triangle 
minus the area of triangle 
. Using the area formula 
to compute the areas of the two triangles, this is 
, so the answer is 
.
See also
| Mock AIME 4 2006-2007 (Problems, Source) | ||
| Preceded by Problem 3 | Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
