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Saint Petersburg Mathematical Olympiad
2014 Saint Petersburg Mathematical Olympiad
3
Some geometry
Some geometry
Source: St Petersburg Olympiad 2014, Grade 10, P3
October 26, 2017
geometry
Problem Statement
D
D
D
is inner point of triangle
A
B
C
ABC
A
BC
.
E
E
E
is on
B
D
BD
B
D
and
C
E
=
B
D
CE=BD
CE
=
B
D
.
∠
A
B
D
=
∠
E
C
D
=
10
,
∠
B
A
D
=
40
,
∠
C
E
D
=
60
\angle ABD=\angle ECD=10,\angle BAD=40,\angle CED=60
∠
A
B
D
=
∠
EC
D
=
10
,
∠
B
A
D
=
40
,
∠
CE
D
=
60
Prove, that
A
B
>
A
C
AB>AC
A
B
>
A
C
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