shubhamsrg
  • shubhamsrg
If 8 points in a plane are chosen to lie on or inside a circle of diameter 2cm then show that the distance between some two points will be less than 1cm. how should i proceed for this?
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
*
shubhamsrg
  • shubhamsrg
will this help ? suppose a pointP at random is chosen at a distance <1 from O taking P as center and constructing a circle of radius 1, shaded reigon is the common region ,,as P gets closer to O,,space in which any other point can lie becomes lesser.. but how do i prove whole cirlce gets shaded after max 7 points ?
shubhamsrg
  • shubhamsrg
|dw:1344942451700:dw|

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anonymous
  • anonymous
hmm is there a definition for the points? what if all the eight points are on the circle and spaced closely.
shubhamsrg
  • shubhamsrg
well we have to prove there'll be min 2 of those 8 points which will have separation less than 1 cm..
anonymous
  • anonymous
oh i read the question wrong, sorry. i will try it again.
anonymous
  • anonymous
Area of the circle must be \(\pi\). Each point could be imagined as a circle of area \(\pi/4\), maybe?
shubhamsrg
  • shubhamsrg
i dont get it?? come again..
anonymous
  • anonymous
|dw:1344946376091:dw| like you see there are maximum 7 points with distance >=1. If I put one more point it's distance with some point will be less than 1
anonymous
  • anonymous
@Ishaan94 @shubhamsrg
anonymous
  • anonymous
got it?
anonymous
  • anonymous
|dw:1344946685043:dw|
shubhamsrg
  • shubhamsrg
cool.. maybe this is satisfactory enough!! thanks..
anonymous
  • anonymous
yw

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