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Austrian MO National Competition
2004 Federal Competition For Advanced Students, Part 1
2
2
Part of
2004 Federal Competition For Advanced Students, Part 1
Problems
(1)
Three pairs of perpendicular diagonals (Austria 2004 -Part1)
Source:
6/18/2011
A convex hexagon
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
with
A
B
=
B
C
=
a
,
C
D
=
D
E
=
b
,
E
F
=
F
A
=
c
AB = BC = a, CD = DE = b, EF = FA = c
A
B
=
BC
=
a
,
C
D
=
D
E
=
b
,
EF
=
F
A
=
c
is inscribed in a circle. Show that this hexagon has three (pairwise disjoint) pairs of mutually perpendicular diagonals.