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Problem
Problem
Consider a
Δ
A
B
C
\Delta ABC
Δ
A
B
C
and points
A
1
A_1
A
1
and
B
1
B_1
B
1
on side
B
C
BC
B
C
such that
∠
B
A
A
1
=
∠
B
1
A
C
\angle BAA_1 = \angle B_1AC
∠
B
A
A
1
=
∠
B
1
A
C
. If incircle of
Δ
B
A
A
1
\Delta BAA_1
Δ
B
A
A
1
and
B
1
A
C
B_1AC
B
1
A
C
touch the sides
B
A
1
BA_1
B
A
1
and
B
1
C
B_1C
B
1
C
at
M
M
M
and
N
N
N
respectively, prove that
1
B
M
+
1
M
A
1
=
1
B
1
N
+
1
N
C
\frac{1}{BM} + \frac{1}{MA_1} = \frac{1}{B_1N} + \frac{1}{NC}
B
M
1
+
M
A
1
1
=
B
1
N
1
+
N
C
1
.
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