1989 OIM Problems/Problem 4
Problem
The circumference inscribed in triangle 
, is tangent to sides 
and 
at points 
and 
respectively. The bisectors of 
and 
intersect 
at points 
and 
respectively. Let 
be the incenter of triangle . Prove:
![\[(MP)(OA)=(BC)(OQ)\]](http://latex.artofproblemsolving.com/d/5/a/d5a9f607e5b2ddc7b26d7b59ef3d6eaa8acfed44.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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