Well for a circle, if you know the centre, just use a simple distance calculation to determine if it's inside it. If you need only a 'slice' (or beam as you mentioned) to be detected, get the two angles of the line segments from centre and determine if it's within those.

I don't have my AdvancedMath.pas unit handy or I'd throw up the function for you.

For your solution you'd need to compare distance then determine the angle of the object to your sentry object's beam emitter. Once you have all of that information, just use the angles of your beam arcs and the rest is comparison. Just be 0/360 conscious when doing your angle range checks.