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Spain Contests
Spain Mathematical Olympiad
2013 Spain Mathematical Olympiad
6
6
Part of
2013 Spain Mathematical Olympiad
Problems
(1)
Characterize the convex quadrilateral
Source: Spanish Mathematical Olympiad 2013. Problem 6.
3/26/2015
Let
A
B
C
D
ABCD
A
BC
D
a convex quadrilateral where:
∣
A
B
∣
+
∣
C
D
∣
=
2
∣
A
C
∣
|AB|+|CD|=\sqrt{2} |AC|
∣
A
B
∣
+
∣
C
D
∣
=
2
∣
A
C
∣
and
∣
B
C
∣
+
∣
D
A
∣
=
2
∣
B
D
∣
|BC|+|DA|=\sqrt{2} |BD|
∣
BC
∣
+
∣
D
A
∣
=
2
∣
B
D
∣
What form does the quadrilateral have?
geometry