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National and Regional Contests
Singapore Contests
Singapore Senior Math Olympiad
2012 Singapore Senior Math Olympiad
1
1
Part of
2012 Singapore Senior Math Olympiad
Problems
(1)
pure geometry-prove
Source:
2/22/2015
A circle
ω
\omega
ω
through the incentre
I
I
I
of a triangle
A
B
C
ABC
A
BC
and tangent to
A
B
AB
A
B
at
A
A
A
, intersects the segment
B
C
BC
BC
at
D
D
D
and the extension of
B
C
BC
BC
at
E
E
E
. Prove that the line
I
C
IC
I
C
intersects
ω
\omega
ω
at a point
M
M
M
such that
M
D
=
M
E
MD=ME
M
D
=
ME
.
geometry
incenter
symmetry
geometry unsolved