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JOM 2015 Shortlist
G6
G6
Part of
JOM 2015 Shortlist
Problems
(1)
BE, CF, PR concurrent
Source: Junior Olympiad of Malaysia Shortlist 2015 G6
7/17/2015
Let
A
B
C
ABC
A
BC
be a triangle. Let
ω
1
\omega_1
ω
1
be circle tangent to
B
C
BC
BC
at
B
B
B
and passes through
A
A
A
. Let
ω
2
\omega_2
ω
2
be circle tangent to
B
C
BC
BC
at
C
C
C
and passes through
A
A
A
. Let
ω
1
\omega_1
ω
1
and
ω
2
\omega_2
ω
2
intersect again at
P
≠
A
P \neq A
P
=
A
. Let
ω
1
\omega_1
ω
1
intersect
A
C
AC
A
C
again at
E
≠
A
E\neq A
E
=
A
, and let
ω
2
\omega_2
ω
2
intersect
A
B
AB
A
B
again at
F
≠
A
F\neq A
F
=
A
. Let
R
R
R
be the reflection of
A
A
A
about
B
C
BC
BC
, Prove that lines
B
E
,
C
F
,
P
R
BE, CF, PR
BE
,
CF
,
PR
are concurrent.
geometry