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Problems
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International Contests
Tuymaada Olympiad
1994 Tuymaada Olympiad
3
3
Part of
1994 Tuymaada Olympiad
Problems
(1)
M,N interior points of triangle ABC, prove that AN>AM or BN>BM or CN>CM
Source: Tuymaada 1994 p3
9/28/2018
Point
M
M
M
lies inside triangle
A
B
C
ABC
A
BC
. Prove that for any other point
N
N
N
lying inside the triangle
A
B
C
ABC
A
BC
, at least one of the following three inequalities is fulfilled:
A
N
>
A
M
,
B
N
>
B
M
,
C
N
>
C
M
AN>AM, BN>BM, CN>CM
A
N
>
A
M
,
BN
>
BM
,
CN
>
CM
.
geometry
geometric inequality