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Topic
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2012-2013 Winter OMO #38
v_Enhance 11
N
by PEKKA
Triangle 
has sides 
, 
, and 
. Let 
be the points on segments 
, respectively, such that 
and 
. Suppose lines 
and 
intersect at 
and the circumcircles of 
and 
intersect at a second point 
. If the length of segment 
can be expressed in the form 
for positive integers 
, where 
is not divisible by the square of any prime, find 
.
Victor Wang
has sides 
, 
, and 
. Let 
be the points on segments 
, respectively, such that 
and 
. Suppose lines 
and 
intersect at 
and the circumcircles of 
and 
intersect at a second point 
. If the length of segment 
can be expressed in the form 
for positive integers 
, where 
is not divisible by the square of any prime, find 
.Victor Wang
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