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Moldova Contests
Moldova Team Selection Test
2018 Moldova Team Selection Test
11
11
Part of
2018 Moldova Team Selection Test
Problems
(1)
Geometry problem
Source: Moldova TST 2018
4/6/2018
Let
Ω
\Omega
Ω
be the circumcincle of the quadrilateral
A
B
C
D
ABCD
A
BC
D
, and
E
E
E
the intersection point of the diagonals
A
C
AC
A
C
and
B
D
BD
B
D
. A line passing through
E
E
E
intersects
A
B
AB
A
B
and
B
C
BC
BC
in points
P
P
P
and
Q
Q
Q
. A circle ,that is passing through point
D
D
D
, is tangent to the line
P
Q
PQ
PQ
in point
E
E
E
and intersects
Ω
\Omega
Ω
in point
R
R
R
, different from
D
D
D
. Prove that the points
B
,
P
,
Q
,
B,P,Q,
B
,
P
,
Q
,
and
R
R
R
are concyclic .
geometry