MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
1993 All-Russian Olympiad Regional Round
10.1
10.1
Part of
1993 All-Russian Olympiad Regional Round
Problems
(1)
AN = 2KM if AK = BK - All-Russian MO 1993 Regional (R4) 10.1
Source:
8/26/2024
Point
D
D
D
is chosen on the side
A
C
AC
A
C
of an acute-angled triangle
A
B
C
ABC
A
BC
. The median
A
M
AM
A
M
intersects the altitude
C
H
CH
C
H
and the segment
B
D
BD
B
D
at points
N
N
N
and
K
K
K
respectively. Prove that if
A
K
=
B
K
AK = BK
A
K
=
B
K
, then
A
N
=
2
K
M
AN = 2KM
A
N
=
2
K
M
.
geometry
equal segments