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National and Regional Contests
India Contests
India National Olympiad
2017 India National Olympiad
4
4
Part of
2017 India National Olympiad
Problems
(1)
Convex pentagon with consecutive integer lengths
Source: INMO Problem 4
1/15/2017
Let
A
B
C
D
E
ABCDE
A
BC
D
E
be a convex pentagon in which
∠
A
=
∠
B
=
∠
C
=
∠
D
=
12
0
∘
\angle{A}=\angle{B}=\angle{C}=\angle{D}=120^{\circ}
∠
A
=
∠
B
=
∠
C
=
∠
D
=
12
0
∘
and the side lengths are five consecutive integers in some order. Find all possible values of
A
B
+
B
C
+
C
D
AB+BC+CD
A
B
+
BC
+
C
D
.
geometry