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National and Regional Contests
Mexico Contests
Mexico National Olympiad
2016 Mexico National Olmypiad
1
1
Part of
2016 Mexico National Olmypiad
Problems
(1)
Prove QR=RT
Source: Mexican Mathematical Olympiad 2016
11/7/2016
Let
C
1
C_1
C
1
and
C
2
C_2
C
2
be two circumferences externally tangents at
S
S
S
such that the radius of
C
2
C_2
C
2
is the triple of the radius of
C
1
C_1
C
1
. Let a line be tangent to
C
1
C_1
C
1
at
P
≠
S
P \neq S
P
=
S
and to
C
2
C_2
C
2
at
Q
≠
S
Q \neq S
Q
=
S
. Let
T
T
T
be a point on
C
2
C_2
C
2
such that
Q
T
QT
QT
is diameter of
C
2
C_2
C
2
. Let the angle bisector of
∠
S
Q
T
\angle SQT
∠
SQT
meet
S
T
ST
ST
at
R
R
R
. Prove that
Q
R
=
R
T
QR=RT
QR
=
RT
geometry