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All-Russian Olympiad
1970 All Soviet Union Mathematical Olympiad
135
135
Part of
1970 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 135 All Soviet Union MO 1970 median, bisector, height concurrent
Source:
6/24/2019
The angle bisector
[
A
D
]
[AD]
[
A
D
]
, the median
[
B
M
]
[BM]
[
BM
]
and the height
[
C
H
]
[CH]
[
C
H
]
of the acute-angled triangle
A
B
C
ABC
A
BC
intersect in one point. Prove that the
∠
B
A
C
>
4
5
o
\angle BAC> 45^o
∠
B
A
C
>
4
5
o
.
geometry
median
concurrent
angle bisector
altitude