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Greece Junior National Olympiad 1997-98 Pronlem 4

Source:

August 10, 2015

geometry

Problem Statement

Let

K(O,R)

be a circle with center

O

and radious

R

and

(e)

to be a line thst tangent to

K

at

A

. A line parallel to

OA

cuts

K

at

B, C

, and

(e)

at

D

, (

C

is between

B

and

D

). Let

E

to be the antidiameric of

C

with respect to

K

.

EA

cuts

BD

at

F

.
i)Examine if

CEF

is isosceles. ii)Prove that

2AD=EB

. iii)If

K

si the midlpoint of

CF

, prove that

AB=KO

. iv)If

R=\frac{5}{2}, AD=\frac{3}{2}

, calculate the area of

EBF

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