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Greece Junior Math Olympiad
2011 Greece Junior Math Olympiad
1
1
Part of
2011 Greece Junior Math Olympiad
Problems
(1)
<A=120^o, median AD perpendicular to side AB (Greece Junior 2011)
Source:
7/14/2019
Let
A
B
C
ABC
A
BC
be a triangle with
∠
B
A
C
=
12
0
o
\angle BAC=120^o
∠
B
A
C
=
12
0
o
, which the median
A
D
AD
A
D
is perpendicular to side
A
B
AB
A
B
and intersects the circumscribed circle of triangle
A
B
C
ABC
A
BC
at point
E
E
E
. Lines
B
A
BA
B
A
and
E
C
EC
EC
intersect at
Z
Z
Z
. Prove that a)
Z
D
⊥
B
E
ZD \perp BE
Z
D
⊥
BE
b)
Z
D
=
B
C
ZD=BC
Z
D
=
BC
geometry
perpendicular
circumcircle