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 2 years ago
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.
 2 years ago
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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cwrw238
 2 years ago
Best ResponseYou've already chosen the best response.0the locus is a circle  can you say what its radius is?

aroub
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, I can. But only if you told me how did you get it and which circle?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1keeping O,N and M are collinear. means a fixed length (like a stick)

phi
 2 years ago
Best ResponseYou've already chosen the best response.1if M traces out the outer circle, what does the rest of the "stick" do?

aroub
 2 years ago
Best ResponseYou've already chosen the best response.0Another circle? With radius OM?

cwrw238
 2 years ago
Best ResponseYou've already chosen the best response.0no the radius is ON + (MN/2)  do you see why?

aroub
 2 years ago
Best ResponseYou've already chosen the best response.0The other circle that will be formed is it like this? dw:1352053569404:dw

aroub
 2 years ago
Best ResponseYou've already chosen the best response.0Great :D So how did you get the radius? It's OM + MN?

cwrw238
 2 years ago
Best ResponseYou've already chosen the best response.0no!!! sorry  the circle rund in between the 2 original circles

phi
 2 years ago
Best ResponseYou've already chosen the best response.1The 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
 2 years ago
Best ResponseYou've already chosen the best response.0But 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
 2 years ago
Best ResponseYou've already chosen the best response.0Aooh, wait! phi's answer makes more sense :P So it makes two other circles or just the circle between?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1you 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?

aroub
 2 years ago
Best ResponseYou've already chosen the best response.0The "smear" will be between the two circles forming a circle, right?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1yes the radius is the "average" of ON and OM or (ON + OM)/2 which is the same as ON + NM/2

aroub
 2 years ago
Best ResponseYou've already chosen the best response.0This 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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