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APMO
2016 APMO
3
3
Part of
2016 APMO
Problems
(1)
APMO 2016: Line is tangent to circle
Source: APMO 2016, problem 3
5/16/2016
Let
A
B
AB
A
B
and
A
C
AC
A
C
be two distinct rays not lying on the same line, and let
ω
\omega
ω
be a circle with center
O
O
O
that is tangent to ray
A
C
AC
A
C
at
E
E
E
and ray
A
B
AB
A
B
at
F
F
F
. Let
R
R
R
be a point on segment
E
F
EF
EF
. The line through
O
O
O
parallel to
E
F
EF
EF
intersects line
A
B
AB
A
B
at
P
P
P
. Let
N
N
N
be the intersection of lines
P
R
PR
PR
and
A
C
AC
A
C
, and let
M
M
M
be the intersection of line
A
B
AB
A
B
and the line through
R
R
R
parallel to
A
C
AC
A
C
. Prove that line
M
N
MN
MN
is tangent to
ω
\omega
ω
.Warut Suksompong, Thailand
geometry