2001 AIME I Problems/Problem 4
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Problem
In triangle 
, angles 
and 
measure 
degrees and 
degrees, respectively. The bisector of angle intersects 
at 
, and 
. The area of triangle can be written in the form 
, where 
, 
, and 
are positive integers, and is not divisible by the square of any prime. Find 
.
Solution
Let 
be the foot of the altitude from 
to 
. By simple angle-chasing, we find that 
, and thus 
. Now 
is a 
right triangle and 
is a 
right triangle, so 
. The area of
and the answer is 
.
See also
| 2001 AIME I (Problems • Resources) | ||
| Preceded by Problem 3 | Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
