making extruded cut in larger cylinder for smaller cylinder to slip into

Hello All,

I'm trying to make an extruded cut in a large cylinder where a smaller cylinder intersects.  I arbitrarily made a 24o.d. x 1/2 wall cylinder with a 18o.d. x 1/2 wall cylinder going into it at a 90.  I made a plane and offset it 36" from centerline of big tube for where the smaller tube must extend outward to.  Then I extruded the smaller tube "up to body" on the larger.  Then used "intersect curve" to get the curve on the outside for cutting out. 

Would the best way to make the cut be to just use "offset from surface" and then just have it go like 2" inward towards center so that it would only cut out the one side of larger cylinder?  I obviously don't want the cutout to go thru the other end so not sure which end condition is the best to use in this case.  I used "offset from surface" and picked the larger cylinder and it appears to work but this may not be the correct/ideal one to use.  Thanks for any input!