Needle with point around figure's side (10)
I believe the answer is:
hypotenuse
'side' is the definition.
(side of a triangle)
'needle with point around figure's' is the wordplay.
'needle' becomes 'hypo' (hypodermic needle).
'with' is an insertion indicator.
'point' becomes 'S' (S is an example).
'around figure' becomes 'tenue' (I can't explain this - if you can you should give a lot more credence to this answer).
's' placed within 'tenue' is 'tenuse'.
'hypo'+'tenuse'='HYPOTENUSE'
(Other definitions for hypotenuse that I've seen before include "Longest side of right-angled triangle" , "Side opposite right angle" , "geometrician's line" , "Subject of 1 across's theorem" , "Right-angled triangle's longest side" .)