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Problems
Contests
International Contests
IMO Shortlist
1978 IMO Shortlist
7
7
Part of
1978 IMO Shortlist
Problems
(1)
Prove the existence and uniqueness of three points
Source:
9/20/2010
We consider three distinct half-lines
O
x
,
O
y
,
O
z
Ox, Oy, Oz
O
x
,
O
y
,
O
z
in a plane. Prove the existence and uniqueness of three points
A
∈
O
x
,
B
∈
O
y
,
C
∈
O
z
A \in Ox, B \in Oy, C \in Oz
A
∈
O
x
,
B
∈
O
y
,
C
∈
O
z
such that the perimeters of the triangles
O
A
B
,
O
B
C
,
O
C
A
OAB,OBC,OCA
O
A
B
,
OBC
,
OC
A
are all equal to a given number
2
p
>
0.
2p > 0.
2
p
>
0.
geometry
Triangle
IMO Shortlist