MathDB

Problem 4

Source: Greek M.O. 2014

April 13, 2014

projective geometrygeometrycyclic quadrilateralgeometry unsolved

Problem Statement

We are given a circle

c(O,R)

and two points

A,B

so that

R<AB<2R

.The circle

c_1 (A,r)

(

0<r<R

) crosses the circle

c

at C,D (

C

belongs to the short arc

AB

).From

B

we consider the tangent lines

BE,BF

to the circle

c_1

,in such way that

E

lays out of the circle

c

.If

M\equiv EC\cap DF

show that the quadrilateral

BCFM

is cyclic.

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