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Moscow Mathematical Olympiad
2017 Moscow Mathematical Olympiad
2
2
Part of
2017 Moscow Mathematical Olympiad
Problems
(1)
Incircle geometry
Source: Moscow Math Olympiad 2017, Grade 11, P2
4/25/2017
ω
\omega
ω
is incircle of
△
A
B
C
\triangle ABC
△
A
BC
touch
A
C
AC
A
C
in
S
S
S
. Point
Q
Q
Q
lies on
ω
\omega
ω
and midpoints of
A
Q
AQ
A
Q
and
Q
C
QC
QC
lies on
ω
\omega
ω
. Prove that
Q
S
QS
QS
bisects
∠
A
Q
C
\angle AQC
∠
A
QC
geometry