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National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2000 Junior Balkan Team Selection Tests - Moldova
3
3
Part of
2000 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
2AD <BE + EA for angle bisectors in an isosceles 100-40-40 triangle
Source: Moldova JBMO TST 2000 1.3
7/9/2020
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
=
A
C
AB = AC
A
B
=
A
C
¸
∠
B
A
C
=
10
0
o
\angle BAC = 100^o
∠
B
A
C
=
10
0
o
and
A
D
,
B
E
AD, BE
A
D
,
BE
angle bisectors. Prove that
2
A
D
<
B
E
+
E
A
2AD <BE + EA
2
A
D
<
BE
+
E
A
geometry
angle bisector
geometric inequality
isosceles