MathDB
Problems
Contests
International Contests
Tournament Of Towns
1984 Tournament Of Towns
(054) O2
(054) O2
Part of
1984 Tournament Of Towns
Problems
(1)
TOT 054 1984 Spring J-O2 CD=2AM inside a convex pentagon
Source:
8/19/2019
In the convex pentagon
A
B
C
D
E
ABCDE
A
BC
D
E
,
A
E
=
A
D
AE = AD
A
E
=
A
D
,
A
B
=
A
C
AB = AC
A
B
=
A
C
, and angle
C
A
D
CAD
C
A
D
equals the sum of angles
A
E
B
AEB
A
EB
and
A
B
E
ABE
A
BE
. Prove that segment
C
D
CD
C
D
is double the length of median
A
M
AM
A
M
of triangle
A
B
E
ABE
A
BE
.
geometry
convex
pentagon
equal segments