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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.

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Just a line?
@phi ? :)

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Other answers:

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?
  • phi
keeping O,N and M are collinear. means a fixed length (like a stick)
  • phi
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
  • phi
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?
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?!
Aooh, wait! phi's answer makes more sense :P So it makes two other circles or just the circle between?
  • phi
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
The "smear" will be between the two circles forming a circle, right?
  • phi
yes the radius is the "average" of ON and OM or (ON + OM)/2 which is the same as ON + NM/2
This was my last question in locus ( I think and I really hope so ) You're amazing, I'm not kidding :P I love how you think of locus! Like in a very simple way and understandable. Thank you soooooooo mucchhh!! :D

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