Consider the figure below. Given that the two concentric circles are fixed. Find the locus of midpoint MN as M traces on outer circle, keeping O,N and M are collinear.

Question

aroub · Answer

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aroub · Answer

Just a line?

aroub · Answer

@phi ? :)

cwrw238 · Answer

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

aroub · Answer

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

phi · Answer

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

phi · Answer

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

aroub · Answer

Another circle? With radius OM?

cwrw238 · Answer

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

aroub · Answer

The other circle that will be formed is it like this? 

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aroub · Answer

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

cwrw238 · Answer

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

phi · Answer

The mid point of MN is between points M and N .   As the radius OM traces out a circle, what does that mid point do?

aroub · Answer

But if you thought of it, they said that M traces on the outer circle keeping O,N and M collinear so it forms a circle outside?!

aroub · Answer

Aooh, wait! phi's answer makes more sense :P So it makes two other circles or just the circle between?

phi · Answer

you put a dab of paint on the "stick"  at the point halfway between M and N
where is the "smear" as you turn the stick?

phi · Answer

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