answer fast...........

Let A =x. Draw a perpendicular OD on BC. It can easily be shown that triangles OBD and ODC are congurent. So

BOD=  DOC =(2 x)/2=x ( Angle subtented at centre by an arc is double the correspomding angle subtended at segment)

So we have in triangle BOD,

cosx=BD/OB=BD/5... 1

Also triangles BAD and CAD are congurent.So   BAD=x/2

In triangle BAD,

cos x/2=BD/6...2

Using 1 and 2 we can calculate the values of BD.Consequently,BC=2BD