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Netherlands Contests
Dutch Mathematical Olympiad
1989 Dutch Mathematical Olympiad
2
2
Part of
1989 Dutch Mathematical Olympiad
Problems
(1)
EF tangent to circle (A,EB), <EAF=45^o, ABCD is square
Source: Netherlands - Dutch MO 1989 p2
12/25/2022
Given is a square
A
B
C
D
ABCD
A
BC
D
with
E
∈
B
C
E \in BC
E
∈
BC
, arbitrarily. On
C
D
CD
C
D
lies the point
F
F
F
is such that
∠
E
A
F
=
4
5
o
\angle EAF = 45^o
∠
E
A
F
=
4
5
o
. Prove that
E
F
EF
EF
is tangent to the circle with center
A
A
A
and radius
A
B
AB
A
B
.
square
tangent
geometry