2001 AIME II Problems/Problem 13
From AoPSWiki
Problem
In quadrilateral 
, 
and 
, 
, 
, and 
. The length 
may be written in the form 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
Extend 
and 
to meet at 
. Then, since 
and 
, we know that 
. Hence 
, and 
is isosceles. Then 
.
Using the similarity, we have:
The answer is 
.
Extension: Find 
.
See also
| 2001 AIME II (Problems • Resources) | ||
| Preceded by Problem 12 | Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
