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Saint Petersburg Mathematical Olympiad
2011 Saint Petersburg Mathematical Olympiad
3
Point in triangle
Point in triangle
Source: St Petersburg Olympiad 2011, Grade 9, P3
September 15, 2017
geometry
Problem Statement
Point
D
D
D
is inside
△
A
B
C
\triangle ABC
△
A
BC
and
A
D
=
D
C
AD=DC
A
D
=
D
C
.
B
D
BD
B
D
intersect
A
C
AC
A
C
in
E
E
E
.
B
D
B
E
=
A
E
E
C
\frac{BD}{BE}=\frac{AE}{EC}
BE
B
D
=
EC
A
E
. Prove, that
B
E
=
B
C
BE=BC
BE
=
BC
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