MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2019 India National OIympiad
2
2
Part of
2019 India National OIympiad
Problems
(1)
INMO 2019 P2
Source:
1/20/2019
Let
A
1
B
1
C
1
D
1
E
1
A_1B_1C_1D_1E_1
A
1
B
1
C
1
D
1
E
1
be a regular pentagon.For
2
≤
n
≤
11
2 \le n \le 11
2
≤
n
≤
11
, let
A
n
B
n
C
n
D
n
E
n
A_nB_nC_nD_nE_n
A
n
B
n
C
n
D
n
E
n
be the pentagon whose vertices are the midpoint of the sides
A
n
−
1
B
n
−
1
C
n
−
1
D
n
−
1
E
n
−
1
A_{n-1}B_{n-1}C_{n-1}D_{n-1}E_{n-1}
A
n
−
1
B
n
−
1
C
n
−
1
D
n
−
1
E
n
−
1
. All the
5
5
5
vertices of each of the
11
11
11
pentagons are arbitrarily coloured red or blue. Prove that four points among these
55
55
55
points have the same colour and form the vertices of a cyclic quadrilateral.
combinatorics