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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?
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 ?
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hmm is there a definition for the points? what if all the eight points are on the circle and spaced closely.
well we have to prove there'll be min 2 of those 8 points which will have separation less than 1 cm..
oh i read the question wrong, sorry. i will try it again.
Area of the circle must be \(\pi\). Each point could be imagined as a circle of area \(\pi/4\), maybe?
i dont get it?? come again..
|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
cool.. maybe this is satisfactory enough!! thanks..