Difference between revisions of "1997 OIM Problems/Problem 2"
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Latest revision as of 15:23, 13 December 2023
Problem
With the center at the incenter 
of a triangle 
, a circle is drawn that cuts each of the three sides of the triangle at two points: the segment 
at 
and 
( being the closest to 
); the the segment 
in 
and 
( being the closest to 
), and the segment 
in 
and 
( being the closest to 
).
Let 
be the point of intersection of the diagonals of the quadrilateral 
. Let 
be the point of intersection of the diagonals of the 
quadrilateral. Let 
be the point of intersection of the diagonals of the quadrilateral 
.
Show that the circles circumscribed by the triangles 
, 
and 
have a single common point.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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