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Kosovo Team Selection Test
2016 Kosovo Team Selection Test
5
5
Part of
2016 Kosovo Team Selection Test
Problems
(1)
Kosovo Mathematical Olympiad 2016 TST , Problem 5
Source:
1/9/2017
Let be
A
B
C
ABC
A
BC
an acute triangle with
∣
A
B
∣
>
∣
A
C
∣
|AB|>|AC|
∣
A
B
∣
>
∣
A
C
∣
. Let be
D
D
D
point in side
A
B
AB
A
B
such that
∠
A
C
D
=
∠
C
B
D
\angle ACD=\angle CBD
∠
A
C
D
=
∠
CB
D
. Let be
E
E
E
the midpoint of segment
B
D
BD
B
D
and
S
S
S
let be the circumcenter of triangle
B
C
D
BCD
BC
D
. Show that points
A
,
E
,
S
A,E,S
A
,
E
,
S
and
C
C
C
lie on a circle .
geometry