2019 USAJMO Problems/Problem 4
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Let
be a triangle with
obtuse. The [i]
-excircle[/i] is a circle in the exterior of
that is tangent to side
of the triangle and tangent to the extensions of the other two sides. Let
,
be the feet of the altitudes from
and
to lines
and
, respectively. Can line
be tangent to the
-excircle?