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 2 years ago
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?
 2 years ago
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?

This Question is Closed

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0will 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
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1344942451700:dw

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.1hmm is there a definition for the points? what if all the eight points are on the circle and spaced closely.

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0well we have to prove there'll be min 2 of those 8 points which will have separation less than 1 cm..

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.1oh i read the question wrong, sorry. i will try it again.

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.1Area of the circle must be \(\pi\). Each point could be imagined as a circle of area \(\pi/4\), maybe?

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0i dont get it?? come again..

myko
 2 years ago
Best ResponseYou've already chosen the best response.2dw: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

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0cool.. maybe this is satisfactory enough!! thanks..
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