MathDB
Problems
Contests
National and Regional Contests
Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2007 Bosnia and Herzegovina Junior BMO TST
4
4
Part of
2007 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
< IMA = <INB, incenter and arc midpoint of circumcircle related
Source: 2007 Bosnia & Herzegovina JBMO TST p4
5/27/2020
Let
I
I
I
be the incenter of the triangle
A
B
C
ABC
A
BC
(
A
B
<
B
C
AB < BC
A
B
<
BC
). Let
M
M
M
be the midpoint of
A
C
AC
A
C
, and let
N
N
N
be the midpoint of the arc
A
C
AC
A
C
of the circumcircle of
A
B
C
ABC
A
BC
which contains
B
B
B
. Prove that
∠
I
M
A
=
∠
I
N
B
\angle IMA = \angle INB
∠
I
M
A
=
∠
I
NB
.
geometry
circumcircle
incenter
arc midpoint
equal angles