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Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2020 Junior Balkan Team Selection Tests - Moldova
11
11
Part of
2020 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
JBMO TST 2020 - Moldova P11
Source: JBMO TST 2020 Moldova
10/13/2020
Let
△
A
B
C
\triangle ABC
△
A
BC
be an acute triangle. The bisector of
∠
A
C
B
\angle ACB
∠
A
CB
intersects side
A
B
AB
A
B
in
D
D
D
. The circumcircle of triangle
A
D
C
ADC
A
D
C
intersects side
B
C
BC
BC
in
C
C
C
and
E
E
E
with
C
≠
E
C \neq E
C
=
E
. The line parallel to
A
E
AE
A
E
which passes through
B
B
B
intersects line
C
D
CD
C
D
in
F
F
F
. Prove that the triangle
△
A
F
B
\triangle AFB
△
A
FB
is isosceles.
geometry
circumcircle