MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
1997 All-Russian Olympiad Regional Round
8.3
8.3
Part of
1997 All-Russian Olympiad Regional Round
Problems
(1)
DA + AE = KC +CM = AB=BC=CA - All-Russian MO 1997 Regional (R4) 8.3
Source:
9/23/2024
On sides
A
B
AB
A
B
and
B
C
BC
BC
of an equilateral triangle
A
B
C
ABC
A
BC
are taken points
D
D
D
and
K
K
K
, and on the side
A
C
AC
A
C
, points
E
E
E
and
M
M
M
so that
D
A
+
A
E
=
K
C
+
C
M
=
A
B
DA + AE = KC +CM = AB
D
A
+
A
E
=
K
C
+
CM
=
A
B
. Prove that the angle between lines
D
M
DM
D
M
and
K
E
KE
K
E
is equal to
6
0
o
60^o
6
0
o
.
geometry
angles
Equilateral