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Rioplatense Mathematical Olympiad, Level 3
2017 Rioplatense Mathematical Olympiad, Level 3
5
5
Part of
2017 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
QP bisects <AQC
Source: : Rioplatense 2017 L3 P5
9/19/2022
Let
A
B
C
ABC
A
BC
be a triangle and
I
I
I
is your incenter, let
P
P
P
be a point in
A
C
AC
A
C
such that
P
I
PI
P
I
is perpendicular to
A
C
AC
A
C
, and let
D
D
D
be the reflection of
B
B
B
wrt circumcenter of
△
A
B
C
\triangle ABC
△
A
BC
. The line
D
I
DI
D
I
intersects again the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
in the point
Q
Q
Q
. Prove that
Q
P
QP
QP
is the angle bisector of the angle
∠
A
Q
C
\angle AQC
∠
A
QC
.
geometry
angles