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Iran MO (2nd Round)
1996 Iran MO (2nd round)
3
3
Part of
1996 Iran MO (2nd round)
Problems
(1)
Mnp right triangle
Source: 14-th Iranian Mathematical Olympiad 1996/1997
10/17/2005
Let
N
N
N
be the midpoint of side
B
C
BC
BC
of triangle
A
B
C
ABC
A
BC
. Right isosceles triangles
A
B
M
ABM
A
BM
and
A
C
P
ACP
A
CP
are constructed outside the triangle, with bases
A
B
AB
A
B
and
A
C
AC
A
C
. Prove that
△
M
N
P
\triangle MNP
△
MNP
is also a right isosceles triangle.
trigonometry
geometry proposed
geometry