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aroub

  • 3 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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  1. aroub
    • 3 years ago
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    |dw:1352052268576:dw|

  2. aroub
    • 3 years ago
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    Just a line?

  3. aroub
    • 3 years ago
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    @phi ? :)

  4. cwrw238
    • 3 years ago
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    the locus is a circle - can you say what its radius is?

  5. aroub
    • 3 years ago
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    Yes, I can. But only if you told me how did you get it and which circle?

  6. phi
    • 3 years ago
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    keeping O,N and M are collinear. means a fixed length (like a stick)

  7. phi
    • 3 years ago
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    if M traces out the outer circle, what does the rest of the "stick" do?

  8. aroub
    • 3 years ago
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    Another circle? With radius OM?

  9. cwrw238
    • 3 years ago
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    no the radius is ON + (MN/2) - do you see why?

  10. aroub
    • 3 years ago
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    The other circle that will be formed is it like this? |dw:1352053569404:dw|

  11. aroub
    • 3 years ago
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    Great :D So how did you get the radius? It's OM + MN?

  12. cwrw238
    • 3 years ago
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    no!!! sorry - the circle rund in between the 2 original circles

  13. phi
    • 3 years ago
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    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?

  14. aroub
    • 3 years ago
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    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?!

  15. aroub
    • 3 years ago
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    Aooh, wait! phi's answer makes more sense :P So it makes two other circles or just the circle between?

  16. phi
    • 3 years ago
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    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?

  17. phi
    • 3 years ago
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    |dw:1352054278598:dw|

  18. aroub
    • 3 years ago
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    The "smear" will be between the two circles forming a circle, right?

  19. phi
    • 3 years ago
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    yes the radius is the "average" of ON and OM or (ON + OM)/2 which is the same as ON + NM/2

  20. aroub
    • 3 years ago
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    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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