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Moldova Contests
Moldova Team Selection Test
2022 Moldova Team Selection Test
6
6
Part of
2022 Moldova Team Selection Test
Problems
(1)
Prove that the lines $BP$ and $CQ$ are perpendicular.
Source: Moldova TST 2022
4/1/2022
Let
A
A
A
be a point outside of the circle
Ω
\Omega
Ω
. Tangents from
A
A
A
touch
Ω
\Omega
Ω
in points
B
B
B
and
C
C
C
. Point
C
C
C
, collinear with
A
A
A
and
P
P
P
, is between
A
A
A
and
P
P
P
, such that the circumcircle of triangle
A
B
P
ABP
A
BP
intersects
Ω
\Omega
Ω
again in point
E
E
E
. Point
Q
Q
Q
is on the segment
B
P
BP
BP
, such that
∠
P
E
Q
=
2
⋅
∠
A
P
B
\angle PEQ=2 \cdot \angle APB
∠
PEQ
=
2
⋅
∠
A
PB
. Prove that the lines
B
P
BP
BP
and
C
Q
CQ
CQ
are perpendicular.
geometry