2022 OIM Problems/Problem 5
Problem
Let 
be an acute triangle with circumcircle 
. Let 
and 
be points on the half-plane defined by 
that contains 
, such that 
and 
are tangent to and 
. Let 
and 
be points on the external bisector of 
, such that 
and 
. Let 
be the point of intersection of lines 
and 
. Prove that 
.
Solution
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