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Moldova Contests
Moldova Team Selection Test
2022 Moldova Team Selection Test
11
11
Part of
2022 Moldova Team Selection Test
Problems
(1)
Prove that $P$, $A$, and $Q$ are collinear.
Source: Moldova TST 2022
4/1/2022
Let
Ω
\Omega
Ω
be the circumcircle of triangle
A
B
C
ABC
A
BC
such that the tangents to
Ω
\Omega
Ω
in points
B
B
B
and
C
C
C
intersect in
P
P
P
. The squares
A
B
B
1
B
2
ABB_1B_2
A
B
B
1
B
2
and
A
C
C
1
C
2
ACC_1C_2
A
C
C
1
C
2
are constructed on the sides
A
B
AB
A
B
and
A
C
AC
A
C
in the exterior of triangle
A
B
C
ABC
A
BC
, such that the lines
B
1
B
2
B_1B_2
B
1
B
2
and
C
1
C
2
C_1C_2
C
1
C
2
intersect in point
Q
Q
Q
. Prove that
P
P
P
,
A
A
A
, and
Q
Q
Q
are collinear.
geometry