1969 IMO Problems/Problem 4
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A semicircular arc 
is drawn with 
as diameter. 
is a point on other than 
and 
, and 
is the foot of the perpendicular from to . We consider three circles, 
, all tangent to the line . Of these, 
is inscribed in 
, while 
and 
are both tangent to 
and , one on each side of . Prove that 
, and have a second tangent in common.
