MathDB
Problems
Contests
National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2001 Moldova Team Selection Test
10
10
Part of
2001 Moldova Team Selection Test
Problems
(1)
Delta 2.9
Source:
6/28/2020
Let
A
B
C
ABC
A
BC
be a triangle and let
D
D
D
and
E
E
E
be points on sides
A
B
AB
A
B
and
A
C
AC
A
C
, respectively, such that
D
E
∥
B
C
DE \parallel BC
D
E
∥
BC
. Let
P
P
P
be any point interior to triangle
A
D
E
ADE
A
D
E
, and let
F
F
F
and
G
G
G
be the intersections of
D
E
DE
D
E
with the lines
B
P
BP
BP
and
C
P
CP
CP
, respectively. Let
Q
Q
Q
be the second intersection point of the circumcircles of triangles
P
D
G
PDG
P
D
G
and
P
F
E
PFE
PFE
. Prove that the points
A
,
P
,
A,P,
A
,
P
,
and
Q
Q
Q
are collinear.
Delta 2