MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Poland - Second Round
2005 Poland - Second Round
2
In the rhombus ABCD
In the rhombus ABCD
Source:
December 6, 2010
geometry
rhombus
trapezoid
geometry proposed
Problem Statement
A rhombus
A
B
C
D
ABCD
A
BC
D
with
∠
B
A
D
=
6
0
∘
\angle BAD=60^{\circ}
∠
B
A
D
=
6
0
∘
is given. Points
E
E
E
on side
A
B
AB
A
B
and
F
F
F
on side
A
D
AD
A
D
are such that
∠
E
C
F
=
∠
A
B
D
\angle ECF=\angle ABD
∠
ECF
=
∠
A
B
D
. Lines
C
E
CE
CE
and
C
F
CF
CF
respectively meet line
B
D
BD
B
D
at
P
P
P
and
Q
Q
Q
. Prove that
P
Q
E
F
=
A
B
B
D
\frac{PQ}{EF}=\frac{AB}{BD}
EF
PQ
=
B
D
A
B
.
Back to Problems
View on AoPS