MathDB
Problems
Contests
International Contests
Iranian Geometry Olympiad
2021 Iranian Geometry Olympiad
2
IGO 2021 P2
IGO 2021 P2
Source: intermediate p2
December 30, 2021
IGO
geometry
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a parallelogram. Points
E
,
F
E, F
E
,
F
lie on the sides
A
B
,
C
D
AB, CD
A
B
,
C
D
respectively, such that
∠
E
D
C
=
∠
F
B
C
\angle EDC = \angle FBC
∠
E
D
C
=
∠
FBC
and
∠
E
C
D
=
∠
F
A
D
\angle ECD = \angle FAD
∠
EC
D
=
∠
F
A
D
. Prove that
A
B
≥
2
B
C
AB \geq 2BC
A
B
≥
2
BC
.Proposed by Pouria Mahmoudkhan Shirazi - Iran
Back to Problems
View on AoPS