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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.
 one year ago
 one year 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.
 one year ago
 one year ago

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cwrw238Best ResponseYou've already chosen the best response.0
the locus is a circle  can you say what its radius is?
 one year ago

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

phiBest ResponseYou've already chosen the best response.1
keeping O,N and M are collinear. means a fixed length (like a stick)
 one year ago

phiBest ResponseYou've already chosen the best response.1
if M traces out the outer circle, what does the rest of the "stick" do?
 one year ago

aroubBest ResponseYou've already chosen the best response.0
Another circle? With radius OM?
 one year ago

cwrw238Best ResponseYou've already chosen the best response.0
no the radius is ON + (MN/2)  do you see why?
 one year ago

aroubBest ResponseYou've already chosen the best response.0
The other circle that will be formed is it like this? dw:1352053569404:dw
 one year ago

aroubBest ResponseYou've already chosen the best response.0
Great :D So how did you get the radius? It's OM + MN?
 one year ago

cwrw238Best ResponseYou've already chosen the best response.0
no!!! sorry  the circle rund in between the 2 original circles
 one year ago

phiBest ResponseYou've already chosen the best response.1
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?
 one year ago

aroubBest ResponseYou've already chosen the best response.0
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?!
 one year ago

aroubBest ResponseYou've already chosen the best response.0
Aooh, wait! phi's answer makes more sense :P So it makes two other circles or just the circle between?
 one year ago

phiBest ResponseYou've already chosen the best response.1
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?
 one year ago

aroubBest ResponseYou've already chosen the best response.0
The "smear" will be between the two circles forming a circle, right?
 one year ago

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

aroubBest ResponseYou've already chosen the best response.0
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
 one year ago
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