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Chile Contests
Chile National Olympiad
2015 Chile National Olympiad
5
5
Part of
2015 Chile National Olympiad
Problems
(1)
given cyclic ABCD with metric relations + angle, find radius (Chile 2015 L1 P5)
Source:
5/26/2019
A quadrilateral
A
B
C
D
ABCD
A
BC
D
is inscribed in a circle. Suppose that
∣
D
A
∣
=
∣
B
C
∣
=
2
|DA| =|BC|= 2
∣
D
A
∣
=
∣
BC
∣
=
2
and
∣
A
B
∣
=
4
|AB| = 4
∣
A
B
∣
=
4
. Let
E
E
E
be the intersection point of lines
B
C
BC
BC
and
D
A
DA
D
A
. Suppose that
∠
A
E
B
=
6
0
o
\angle AEB = 60^o
∠
A
EB
=
6
0
o
and that
∣
C
D
∣
<
∣
A
B
∣
|CD| <|AB|
∣
C
D
∣
<
∣
A
B
∣
. Calculate the radius of the circle.
geometry
cyclic quadrilateral
radius