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International Contests
Baltic Way
2011 Baltic Way
15
15
Part of
2011 Baltic Way
Problems
(1)
Angle EBA is equal to Angle DCB
Source: Baltic Way 2011
11/6/2011
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral such that
∠
A
D
B
=
∠
B
D
C
\angle ADB=\angle BDC
∠
A
D
B
=
∠
B
D
C
. Suppose that a point
E
E
E
on the side
A
D
AD
A
D
satisfies the equality
A
E
⋅
E
D
+
B
E
2
=
C
D
⋅
A
E
.
AE\cdot ED + BE^2=CD\cdot AE.
A
E
⋅
E
D
+
B
E
2
=
C
D
⋅
A
E
.
Show that
∠
E
B
A
=
∠
D
C
B
\angle EBA=\angle DCB
∠
EB
A
=
∠
D
CB
.
geometry proposed
geometry