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|dw:1352052268576:dw|

Just a line?

the locus is a circle - can you say what its radius is?

Yes, I can. But only if you told me how did you get it and which circle?

keeping O,N and M are collinear. means a fixed length (like a stick)

if M traces out the outer circle, what does the rest of the "stick" do?

Another circle? With radius OM?

no the radius is ON + (MN/2)
- do you see why?

The other circle that will be formed is it like this?
|dw:1352053569404:dw|

Great :D So how did you get the radius? It's OM + MN?

no!!! sorry - the circle rund in between the 2 original circles

|dw:1352054278598:dw|

The "smear" will be between the two circles forming a circle, right?

yes
the radius is the "average" of ON and OM or (ON + OM)/2
which is the same as ON + NM/2