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Problems
Contests
National and Regional Contests
Serbia Contests
Serbia JBMO TST
2016 Junior Balkan Team Selection Test
1
1
Part of
2016 Junior Balkan Team Selection Test
Problems
(1)
Serbian Junior TST
Source: Serbia Junior TST 2016 P1
5/21/2016
Let rightangled
△
A
B
C
\triangle ABC
△
A
BC
be given with right angle at vertex
C
C
C
. Let
D
D
D
be foot of altitude from
C
C
C
and let
k
k
k
be circle that touches
B
D
BD
B
D
at
E
E
E
,
C
D
CD
C
D
at
F
F
F
and circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
at
G
G
G
.
a
.
)
a.)
a
.
)
Prove that points
A
A
A
,
F
F
F
and
G
G
G
are collinear.
b
.
)
b.)
b
.
)
Express radius of circle
k
k
k
in terms of sides of
△
A
B
C
\triangle ABC
△
A
BC
.
geometry