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Serbia Contests
Serbia National Math Olympiad
2016 Serbia National Math Olympiad
3
3
Part of
2016 Serbia National Math Olympiad
Problems
(1)
Geometry, SMO 2016, not easy
Source: Serbia National Olympiad 2016, day 1, P3
4/1/2016
Let
A
B
C
ABC
A
BC
be a triangle and
O
O
O
its circumcentre. A line tangent to the circumcircle of the triangle
B
O
C
BOC
BOC
intersects sides
A
B
AB
A
B
at
D
D
D
and
A
C
AC
A
C
at
E
E
E
. Let
A
′
A'
A
′
be the image of
A
A
A
under
D
E
DE
D
E
. Prove that the circumcircle of the triangle
A
′
D
E
A'DE
A
′
D
E
is tangent to the circumcircle of triangle
A
B
C
ABC
A
BC
.
geometry
circumcircle