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2017 Iran MO (2nd Round)
2
2
Part of
2017 Iran MO (2nd Round)
Problems
(1)
Geometry - Iran
Source: Iran National Olympiad 2017, Second Round, Problem 2
4/20/2017
Let
A
B
C
D
ABCD
A
BC
D
be an isosceles trapezoid such that
A
B
∥
C
D
AB \parallel CD
A
B
∥
C
D
. Suppose that there exists a point
P
P
P
in
A
B
C
D
ABCD
A
BC
D
such that
∠
A
P
B
>
∠
A
D
C
\angle APB > \angle ADC
∠
A
PB
>
∠
A
D
C
and
∠
D
P
C
>
∠
A
B
C
\angle DPC > \angle ABC
∠
D
PC
>
∠
A
BC
. Prove that
A
B
+
C
D
>
D
A
+
B
C
.
AB+CD>DA+BC.
A
B
+
C
D
>
D
A
+
BC
.
geometry
trapezoid