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National and Regional Contests
Morocco Contests
Morocco National Olympiad
2005 Morocco National Olympiad
1
1
Part of
2005 Morocco National Olympiad
Problems
(1)
square and tangent line
Source: Moroccan Olympiad 2005 Problem 1
3/12/2005
In a square
A
B
C
D
ABCD
A
BC
D
let
F
F
F
be the midpoint of
[
C
D
]
\left[ CD\right]
[
C
D
]
and let
E
E
E
be a point on
[
A
B
]
\left[ AB\right]
[
A
B
]
such that
A
E
>
E
B
AE>EB
A
E
>
EB
. the parallel with
(
D
E
)
\left( DE\right)
(
D
E
)
passing by
F
F
F
meets the segment
[
B
C
]
\left[ BC\right]
[
BC
]
at
H
H
H
. Prove that the line
(
E
H
)
\left( EH\right)
(
E
H
)
is tangent to the circle circumscribed with
A
B
C
D
ABCD
A
BC
D
geometry