MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
1996 All-Russian Olympiad Regional Round
8.3
8.3
Part of
1996 All-Russian Olympiad Regional Round
Problems
(1)
5 obtuse angles, convex pentagon - All-Russian MO 1996 Regional (R4) 8.3
Source:
9/23/2024
Does such a convex (all angles less than
18
0
o
180^o
18
0
o
) pentagon
A
B
C
D
E
ABCDE
A
BC
D
E
, such that all angles
A
B
D
ABD
A
B
D
,
B
C
E
BCE
BCE
,
C
D
A
CDA
C
D
A
,
D
E
B
DEB
D
EB
and
E
A
C
EAC
E
A
C
are obtuse?
geometry
pentagon
obtuse
angles