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All-Russian Olympiad
1970 All Soviet Union Mathematical Olympiad
138
138
Part of
1970 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 138 All Soviet Union MO 1970 distance equals inradius
Source:
6/24/2019
Given triangle
A
B
C
ABC
A
BC
, midpoint
M
M
M
of the side
[
B
C
]
[BC]
[
BC
]
, the centre
O
O
O
of the inscribed circle. The line
(
M
O
)
(MO)
(
MO
)
crosses the height
A
H
AH
A
H
in the point
E
E
E
. Prove that the distance
∣
A
E
∣
|AE|
∣
A
E
∣
equals the inscribed circle radius.
geometry
incircle
inradius