Junior Balkan MO 2002 - Problem 2
Kvaliteta:
Avg: 0,0Težina:
Avg: 4,0Two circles with centers and
meet at two points
and
such that the centers of the circles are on opposite sides of the line
. The lines
and
meet their respective circles again at
and
. Let
be the midpoint of
. Let
,
be points on the circles of centers
and
respectively, such that
, and
lies on the minor arc
while
lies on the minor arc
. Show that
.
Izvor: Juniorska balkanska matematička olimpijada 2002.