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2014 Harvard-MIT Mathematics Tournament
14
14
Part of
2014 Harvard-MIT Mathematics Tournament
Problems
(1)
2014 Guts #14: Similar, but not Congruent
Source:
4/20/2014
Let
A
B
C
D
ABCD
A
BC
D
be a trapezoid with
A
B
∥
C
D
AB\parallel CD
A
B
∥
C
D
and
∠
D
=
9
0
∘
\angle D=90^\circ
∠
D
=
9
0
∘
. Suppose that there is a point
E
E
E
on
C
D
CD
C
D
such that
A
E
=
B
E
AE=BE
A
E
=
BE
and that triangles
A
E
D
AED
A
E
D
and
C
E
B
CEB
CEB
are similar, but not congruent. Given that
C
D
A
B
=
2014
\tfrac{CD}{AB}=2014
A
B
C
D
=
2014
, find
B
C
A
D
\tfrac{BC}{AD}
A
D
BC
.
geometry
trapezoid