MathDB

4

Part of 2014 Greece National Olympiad

Problems(1)

Problem 4

Source: Greek M.O. 2014

4/13/2014
We are given a circle c(O,R)c(O,R) and two points A,BA,B so that R<AB<2RR<AB<2R.The circle c1(A,r)c_1 (A,r) (0<r<R0<r<R) crosses the circle cc at C,D (CC belongs to the short arc ABAB).From BB we consider the tangent lines BE,BFBE,BF to the circle c1c_1 ,in such way that EE lays out of the circle cc.If M≡EC∩DFM\equiv EC\cap DF show that the quadrilateral BCFMBCFM is cyclic.
projective geometrygeometrycyclic quadrilateralgeometry unsolved