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USA - Middle School Tournaments
Montgomery Blair
MBMT Guts Rounds
2015.24
MBMT Guts #24
MBMT Guts #24
Source:
March 29, 2015
Problem Statement
In cyclic quadrilateral
A
B
C
D
ABCD
A
BC
D
,
∠
D
B
C
=
9
0
∘
\angle DBC = 90^\circ
∠
D
BC
=
9
0
∘
and
∠
C
A
B
=
3
0
∘
\angle CAB = 30^\circ
∠
C
A
B
=
3
0
∘
. The diagonals of
A
B
C
D
ABCD
A
BC
D
meet at
E
E
E
. If
B
E
E
D
=
2
\frac{BE}{ED} = 2
E
D
BE
=
2
and
C
D
=
60
CD = 60
C
D
=
60
, compute
A
D
AD
A
D
. (Note: a cyclic quadrilateral is a quadrilateral that can be inscribed in a circle.)
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