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Armenia National Math Olympiad
2011 Armenian Republican Olympiads
Problem 5
Problem 5
Part of
2011 Armenian Republican Olympiads
Problems
(1)
Problem 2 Day 2
Source: 2011 Armenian Republican Olympiad
8/1/2016
A quadrilateral
A
B
C
D
ABCD
A
BC
D
is such that
∠
A
=
∠
C
=
6
0
o
\angle A= \angle C=60^o
∠
A
=
∠
C
=
6
0
o
and
∠
B
=
10
0
o
\angle B=100^o
∠
B
=
10
0
o
. Let
O
1
O_1
O
1
and
O
2
O_2
O
2
be the centers of the incircles of triangles
A
B
D
ABD
A
B
D
and
C
B
D
CBD
CB
D
respectively. Find the angle between the lines
A
O
2
AO_2
A
O
2
and
C
O
1
CO_1
C
O
1
.
geometry