1969 Canadian MO Problems/Problem 5
From AoPSWiki
Problem
Let 
be a triangle with sides of length 
, 
and 
. Let the bisector of the 
cut 
at 
. Prove that the length of 
is 
Solution
Let 
Note that ![[\triangle ABC]=[\triangle ACD]+[\triangle BCD].](http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/1/1/3/113c0bbee28e372c8363f24ac4fb0461f5043d0b.gif)
This can be rewritten as 
Because 
the expression can be written as 
Dividing by 
as desired.
| 1969 Canadian MO (Problems) | ||
| Preceded by Problem 4 | 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | Followed by Problem 6 |
