When I try to extrude a middle control point it creates a segment which increases the curve length.When I try to fill two selected control points it says " Cannot make segment ". Or is there any other way to create branches to a bezier curve?
No Bezier curves do not branch.
There is a trick to fake it. Select the control point you want to branch from and shift D duplicate it. Actually makes a separate curve, but do not move it, just E extrude out the branch you want.
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Thank you. That is an interesting way to do it which is way better than what i was doing before.Previously I used the snapping tool to place two vertices together.Which is a pain in a 3D world view.I tried your way which works splendidly 
. Thank you for the advice 
. It would have been easier if the extrusion works on bezier curves though!
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