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4
4
Part of
2019 Stanford Mathematics Tournament
Problems
(1)
SMT 2019 Geometry #4 intersecting circles
Source:
8/8/2023
Let
ω
1
\omega_1
ω
1
and
ω
2
\omega_2
ω
2
be two circles intersecting at points
P
P
P
and
Q
Q
Q
. The tangent line closer to
Q
Q
Q
touches
ω
1
\omega_1
ω
1
and
ω
2
\omega_2
ω
2
at
M
M
M
and
N
N
N
respectively. If
P
Q
=
3
P Q = 3
PQ
=
3
,
Q
N
=
2
QN = 2
QN
=
2
, and
M
N
=
P
N
MN = P N
MN
=
PN
, what is
Q
M
2
QM^2
Q
M
2
?
geometry