2023 USAMO Problems/Problem 6
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Problem
Let ABC be a triangle with incenter 
and excenters 
, 
, 
opposite 
, 
, and 
, respectively. Given an arbitrary point 
on the circumcircle of 
that does not lie on any of the lines 
, 
, or 
, suppose the circumcircles of 
and 
intersect at two distinct points and 
. If 
is the intersection of lines 
and , prove that 
.
Solution
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