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National and Regional Contests
Malaysia Contests
Malaysia National Olympiad
2010 Malaysia National Olympiad
7
OMK 2010
OMK 2010
Source:
June 4, 2011
geometry
incenter
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle in which
A
B
=
A
C
AB=AC
A
B
=
A
C
. A point
I
I
I
lies inside the triangle such that
∠
A
B
I
=
∠
C
B
I
\angle ABI=\angle CBI
∠
A
B
I
=
∠
CB
I
and
∠
B
A
I
=
∠
C
A
I
\angle BAI=\angle CAI
∠
B
A
I
=
∠
C
A
I
. Prove that
∠
B
I
A
=
9
0
o
+
∠
C
2
\angle BIA=90^o+\dfrac{\angle C}{2}
∠
B
I
A
=
9
0
o
+
2
∠
C
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