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Regional Mathematical Olympiad
2010 India Regional Mathematical Olympiad
5
Reflection
Reflection
Source:
December 5, 2010
geometry
geometric transformation
reflection
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle in which
∠
A
=
6
0
∘
\angle A = 60^\circ
∠
A
=
6
0
∘
. Let
B
E
BE
BE
and
C
F
CF
CF
be the bisectors of
∠
B
\angle B
∠
B
and
∠
C
\angle C
∠
C
with
E
E
E
on
A
C
AC
A
C
and
F
F
F
on
A
B
AB
A
B
. Let
M
M
M
be the reflection of
A
A
A
in line
E
F
EF
EF
. Prove that
M
M
M
lies on
B
C
BC
BC
.
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