Junior Balkan MO 2003 - Problem 3
Kvaliteta:
Avg: 0,0Težina:
Avg: 4,0Let ,
,
be the midpoints of the arcs
,
,
on the circumcircle of a triangle
not containing the points
,
,
, respectively. Let the line
meets
and
at
and
, and let
be the midpoint of the segment
. Let the line
meet
and
at
and
, and let
be the midpoint of the segment
.
a) Find the angles of triangle ;
b) Prove that if is the point of intersection of the lines
and
, then the circumcenter of triangle
lies on the circumcircle of triangle
.
Izvor: Juniorska balkanska matematička olimpijada 2003.