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Serbia Contests
Serbia JBMO TST
2020 Junior Balkan Team Selection Tests-Serbia
1#
1#
Part of
2020 Junior Balkan Team Selection Tests-Serbia
Problems
(1)
Geometry
Source: Serbia JBMO TST 2020 P1
9/5/2020
Given is triangle
A
B
C
ABC
A
BC
with arbitrary point
D
D
D
on
A
B
AB
A
B
and central of inscribed circle
I
I
I
. The perpendicular bisector of
A
B
AB
A
B
intersects
A
I
AI
A
I
and
B
I
BI
B
I
at
P
P
P
and
Q
Q
Q
, respectively. The circle
(
A
D
P
)
(ADP)
(
A
D
P
)
intersects
C
A
CA
C
A
at
E
E
E
, and the circle
(
B
D
Q
)
(BDQ)
(
B
D
Q
)
intersects
B
C
BC
BC
at
F
F
F
and
(
A
D
P
)
(ADP)
(
A
D
P
)
intersects
(
B
D
Q
)
(BDQ)
(
B
D
Q
)
at
K
K
K
. Prove that
E
,
F
,
K
,
I
E, F, K, I
E
,
F
,
K
,
I
lie on one circle.
geometry