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Problems
Contests
International Contests
International Olympiad of Metropolises
2016 IOM
4
4
Part of
2016 IOM
Problems
(1)
International Olympiad of metropolises 2016 P4
Source: International Olympiad of metropolises 2016
9/7/2016
A convex quadrilateral
A
B
C
D
ABCD
A
BC
D
has right angles at
A
A
A
and
C
C
C
. A point
E
E
E
lies on the extension of the side
A
D
AD
A
D
beyond
D
D
D
so that
∠
A
B
E
=
∠
A
D
C
\angle ABE =\angle ADC
∠
A
BE
=
∠
A
D
C
. The point
K
K
K
is symmetric to the point
C
C
C
with respect to point
A
A
A
. Prove that
∠
A
D
B
=
∠
A
K
E
\angle ADB =\angle AKE
∠
A
D
B
=
∠
A
K
E
.
IOM
geometry