MathDB
Problems
Contests
International Contests
JBMO ShortLists
2005 JBMO Shortlist
5
5
Part of
2005 JBMO Shortlist
Problems
(1)
maximum length in a equilateral, on 2 concentric circles
Source: JBMO Shortlist 2005
1/1/2018
Let
O
O
O
be the center of the concentric circles
C
1
,
C
2
C_1,C_2
C
1
,
C
2
of radii
3
3
3
and
5
5
5
respectively. Let
A
∈
C
1
,
B
∈
C
2
A\in C_1, B\in C_2
A
∈
C
1
,
B
∈
C
2
and
C
C
C
point so that triangle
A
B
C
ABC
A
BC
is equilateral. Find the maximum length of
[
O
C
]
[OC]
[
OC
]
.
geometry
maximum
concentric
Equilateral Triangle