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Kosovo Team Selection Test
2017 Kosovo Team Selection Test
5
5
Part of
2017 Kosovo Team Selection Test
Problems
(1)
2017 Kosovo TST Problem 5
Source:
3/19/2017
Given triangle
A
B
C
ABC
A
BC
. Let
P
P
P
,
Q
Q
Q
,
R
R
R
, be the tangency points of inscribed circle of
△
A
B
C
\triangle ABC
△
A
BC
on sides
A
B
AB
A
B
,
B
C
BC
BC
,
A
C
AC
A
C
respectively. We take the reflection of these points with respect to midpoints of the sides they lie on, and denote them as
P
′
,
Q
′
P',Q'
P
′
,
Q
′
and
R
′
R'
R
′
. Prove that
A
P
′
AP'
A
P
′
,
B
Q
′
BQ'
B
Q
′
, and
C
R
′
CR'
C
R
′
are concurrent.
geometry