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JOM 2015 Shortlist
G3
G3
Part of
JOM 2015 Shortlist
Problems
(1)
A, P, Q are collinear
Source: Junior Olympiad of Malaysia Shortlist 2015 G3
7/17/2015
Let
A
B
C
ABC
A
BC
a triangle. Let
D
D
D
on
A
B
AB
A
B
and
E
E
E
on
A
C
AC
A
C
such that
D
E
∣
∣
B
C
DE||BC
D
E
∣∣
BC
. Let line
D
E
DE
D
E
intersect circumcircle of
A
B
C
ABC
A
BC
at two distinct points
F
F
F
and
G
G
G
so that line segments
B
F
BF
BF
and
C
G
CG
CG
intersect at P. Let circumcircle of
G
D
P
GDP
G
D
P
and
F
E
P
FEP
FEP
intersect again at
Q
Q
Q
. Prove that
A
,
P
,
Q
A, P, Q
A
,
P
,
Q
are collinear.
geometry