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2017 South Africa National Olympiad
2
Determine length of line segment
Determine length of line segment
Source: SAMO 2017 Q2
July 30, 2017
geometry
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a rectangle with side lengths
A
B
=
C
D
=
5
AB = CD = 5
A
B
=
C
D
=
5
and
B
C
=
A
D
=
10
BC = AD = 10
BC
=
A
D
=
10
.
W
,
X
,
Y
,
Z
W, X, Y, Z
W
,
X
,
Y
,
Z
are points on
A
B
,
B
C
,
C
D
AB, BC, CD
A
B
,
BC
,
C
D
and
D
A
DA
D
A
respectively chosen in such a way that
W
X
Y
Z
WXYZ
W
X
Y
Z
is a kite, where
∠
Z
W
X
\angle ZWX
∠
Z
W
X
is a right angle. Given that
W
X
=
W
Z
=
13
WX = WZ = \sqrt{13}
W
X
=
W
Z
=
13
and
X
Y
=
Z
Y
XY = ZY
X
Y
=
Z
Y
, determine the length of
X
Y
XY
X
Y
.
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