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Poland - Second Round
2007 Poland - Second Round
2
Polish MO 2007 Second Round Day 1, problem 2
Polish MO 2007 Second Round Day 1, problem 2
Source:
February 28, 2007
Problem Statement
A
B
C
D
E
ABCDE
A
BC
D
E
is a convex pentagon and:
B
C
=
C
D
,
D
E
=
E
A
,
∠
B
C
D
=
∠
D
E
A
=
9
0
∘
BC=CD, \;\;\; DE=EA, \;\;\; \angle BCD=\angle DEA=90^{\circ}
BC
=
C
D
,
D
E
=
E
A
,
∠
BC
D
=
∠
D
E
A
=
9
0
∘
Prove, that it is possible to build a triangle from segments
A
C
AC
A
C
,
C
E
CE
CE
,
E
B
EB
EB
. Find the value of its angles if
∠
A
C
E
=
α
\angle ACE=\alpha
∠
A
CE
=
α
and
∠
B
E
C
=
β
\angle BEC=\beta
∠
BEC
=
β
.
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