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2020 CMIMC
2020 CMIMC Team
7
7
Part of
2020 CMIMC Team
Problems
(1)
2020 Team 7
Source:
2/2/2020
Points
P
P
P
and
Q
Q
Q
lie on a circle
ω
\omega
ω
. The tangents to
ω
\omega
ω
at
P
P
P
and
Q
Q
Q
intersect at point
T
T
T
, and point
R
R
R
is chosen on
ω
\omega
ω
so that
T
T
T
and
R
R
R
lie on opposite sides of
P
Q
PQ
PQ
and
∠
P
Q
R
=
∠
P
T
Q
\angle PQR = \angle PTQ
∠
PQR
=
∠
PTQ
. Let
R
T
RT
RT
meet
ω
\omega
ω
for the second time at point
S
S
S
. Given that
P
Q
=
12
PQ = 12
PQ
=
12
and
T
R
=
28
TR = 28
TR
=
28
, determine
P
S
PS
PS
.
team
2020