How close to the edge is the hole?
I'd drill the corners (to give your radus)
bigest bit you own on a very slow speed (so you grind it with just the weight if the drill)
Make sure it's on an old bit of wood as it's very easy for the drill to bite and crack the perspex if not fully suported.
Then get a coping saw (blade should have a high tooth count) and cut down the lines nice and slow. (blade perpendicular to the frame)
I hack saw will work to but most don't have the distance between the blade and frame.
File/sand to finish.
I've seen perspex cut with a hot wire too - edges need work, and it smells really bad, but works in a ventilated space.
ultimatehandyman.org have a vid of a guy using a jigsaw (metal cutting blade) cutting acrylic/perspex without any problems
I think the key to using a jigsaw is to start the blade before you make contact and move quickly so the heat from friction isn't consentrated in one place.
Slow and careful is NOT the way to use a jigsaw on wood or plastics