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.