MathDB
Problems
Contests
National and Regional Contests
Malaysia Contests
JOM Shortlists
JOM 2015 Shortlist
G2
G2
Part of
JOM 2015 Shortlist
Problems
(1)
Intersection lies on AM
Source: Junior Olympiad of Malaysia Shortlist 2015 G2
7/17/2015
Let
A
B
C
ABC
A
BC
be a triangle, and let
M
M
M
be midpoint of
B
C
BC
BC
. Let
I
b
I_b
I
b
and
I
c
I_c
I
c
be incenters of
A
M
B
AMB
A
MB
and
A
M
C
AMC
A
MC
. Prove that the second intersection of circumcircles of
A
B
I
b
ABI_b
A
B
I
b
and
A
C
I
c
ACI_c
A
C
I
c
distinct from
A
A
A
lies on line
A
M
AM
A
M
.
geometry