MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2018 India National Olympiad
1
1
Part of
2018 India National Olympiad
Problems
(1)
INMO 2018 -- Problem #1
Source: INMO 2018
1/21/2018
Let
A
B
C
ABC
A
BC
be a non-equilateral triangle with integer sides. Let
D
D
D
and
E
E
E
be respectively the mid-points of
B
C
BC
BC
and
C
A
CA
C
A
; let
G
G
G
be the centroid of
Δ
A
B
C
\Delta{ABC}
Δ
A
BC
. Suppose,
D
D
D
,
C
C
C
,
E
E
E
,
G
G
G
are concyclic. Find the least possible perimeter of
Δ
A
B
C
\Delta{ABC}
Δ
A
BC
.
geometry
Law of Sines