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Cono Sur Olympiad
Cono Sur Shortlist - geometry
2018.G3
2018.G3
Part of
Cono Sur Shortlist - geometry
Problems
(1)
computational in a pentagon ABCDE, AB=AE, AC=AD, <BAE=90^o , <ACB=<ADE=135^o
Source: 2018 Cono Sur Shortlist G3
8/25/2021
Consider the pentagon
A
B
C
D
E
ABCDE
A
BC
D
E
such that
A
B
=
A
E
=
x
AB = AE = x
A
B
=
A
E
=
x
,
A
C
=
A
D
=
y
AC = AD = y
A
C
=
A
D
=
y
,
∠
B
A
E
=
9
0
o
\angle BAE = 90^o
∠
B
A
E
=
9
0
o
and
∠
A
C
B
=
∠
A
D
E
=
13
5
o
\angle ACB = \angle ADE = 135^o
∠
A
CB
=
∠
A
D
E
=
13
5
o
. It is known that
C
C
C
and
D
D
D
are inside the triangle
B
A
E
BAE
B
A
E
. Determine the length of
C
D
CD
C
D
in terms of
x
x
x
and
y
y
y
.
equal angles
geometry
pentagon
equal segments