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5
2013 PUMaC Geometry B5
2013 PUMaC Geometry B5
Source:
November 22, 2013
geometry
trigonometry
Problem Statement
Circle
w
w
w
with center
O
O
O
meets circle
Γ
\Gamma
Γ
at
X
,
Y
,
X,Y,
X
,
Y
,
and
O
O
O
is on
Γ
\Gamma
Γ
. Point
Z
∈
Γ
Z\in\Gamma
Z
∈
Γ
lies outside
w
w
w
such that
X
Z
=
11
XZ=11
XZ
=
11
,
O
Z
=
15
OZ=15
OZ
=
15
, and
Y
Z
=
13
YZ=13
Y
Z
=
13
. If the radius of circle
w
w
w
is
r
r
r
, find
r
2
r^2
r
2
.
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