MathDB
Problems
Contests
National and Regional Contests
India Contests
Regional Mathematical Olympiad
1995 India Regional Mathematical Olympiad
6
6
Part of
1995 India Regional Mathematical Olympiad
Problems
(1)
A 21-gon
Source: Indian RMO 1995 Problem 6
10/26/2005
Let
A
1
A
2
A
3
…
A
21
A_1A_2A_3 \ldots A_{21}
A
1
A
2
A
3
…
A
21
be a 21-sided regular polygon inscribed in a circle with centre
O
O
O
. How many triangles
A
i
A
j
A
k
A_iA_jA_k
A
i
A
j
A
k
,
1
≤
i
<
j
<
k
≤
21
1 \leq i < j < k \leq 21
1
≤
i
<
j
<
k
≤
21
, contain the centre point
O
O
O
in their interior?
geometry
circumcircle
india