________ is to surgery as writer is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

A polygon is convex if, for every pair of points. P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.

Which one of the following is NOT a convex polygon?

Select the word that fits the analogy:

Cook : Cook :: Fly : _____

Raman is confident of speaking English _____ six months as he has been practising regularly_____the last three weeks.