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National and Regional Contests
Moldova Contests
JBMO TST - Moldova
1999 Junior Balkan Team Selection Tests - Moldova
2
2
Part of
1999 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
sum < AEB + <ADB wanted, ABC right isosceles, EC = 2AE given
Source: Moldova JBMO TST 1999 1.2
7/9/2020
Let
A
B
C
ABC
A
BC
be an isosceles right triangle with
∠
A
=
9
0
o
\angle A=90^o
∠
A
=
9
0
o
. Point
D
D
D
is the midpoint of the side
[
A
C
]
[AC]
[
A
C
]
, and point
E
∈
[
A
C
]
E \in [AC]
E
∈
[
A
C
]
is so that
E
C
=
2
A
E
EC = 2AE
EC
=
2
A
E
. Calculate
∠
A
E
B
+
∠
A
D
B
\angle AEB + \angle ADB
∠
A
EB
+
∠
A
D
B
.
geometry
angles
right triangle
isosceles