Please help me with the following problem (I need it as

a lemma):

Given a cyclic quadrilateral ABCD with the circumcenter

O. The perpendicular to BD through B meets the

perpendicular to AC through C at E. The perpendicular

to BD through D meets the perpendicular to AC through A

at F. Finally, let X be the intersection of the lines

AB and CD. Then, the points O, E, F, X are collinear.

Well, it is easy to show that O is the midpoint of EF;

hence, O, E, F are collinear, but how about X ?

Thanks!

Sincerely,

Darij Grinberg