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Serbia JBMO TST
2023 Serbia JBMO TST
1
1
Part of
2023 Serbia JBMO TST
Problems
(1)
Isosceles triangle geo
Source: Serbia JBMO TST 2023 P1
5/28/2023
Given is an isosceles triangle
A
B
C
ABC
A
BC
with
C
A
=
C
B
CA=CB
C
A
=
CB
and angle bisector
B
D
BD
B
D
,
D
ā
A
C
D \in AC
D
ā
A
C
. The line through the center
O
O
O
of
(
A
B
C
)
(ABC)
(
A
BC
)
, perpendicular to
B
D
BD
B
D
, meets
B
C
BC
BC
at
E
E
E
. The line through
E
E
E
, parallel to
B
D
BD
B
D
, meets
A
C
AC
A
C
at
F
F
F
. Prove that
C
E
=
D
F
CE=DF
CE
=
D
F
.
geometry