1Nishant, was it Inaamdar or Bagchi?
There are n points in a plane such that the area of the tirangle formed by any three is less than 1.
Find the "minimum" area in which all these n points are enclosed!!!
This was asked to me in my ISI interview.
*clarification: What is the minimum area in which we can be sure that all these points are enclosed!
** Hint: The shape of the figure with minimum area will be a triangle.
*** More Hint: Draw the traingle of these n points, which will have a maximum area!
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21 Answers
62arrey na... it is not 1...
the area of a single triangle is 1... how can all these points together be in the same area 1?
Refer to the Hints and clarifications above!
62There are n points in a plane such that the area of the tirangle formed by any three is less than 1.
What is the minimum area in which we can be sure that all these points are enclosed!
Hint:
Btw the triange inside is the largest among the n points.
The outer triangle is drawn by drawing parallel lines.
1as i never like to give up.... i will still go on trying.... even if u gv the soln.. i wont see it now... its a nice question... may be others are waiting for d soln... y only wait for me? so.... i dunno if u want u cn post the soln.
1arrey i am sorry..... i cudn proceed with this question... :-( :-( :-(
62ok.. one hint..
The answer is an integer...
Think of some basic theorem of geometry where we used to have equal area of two triangles with same base!
1does my ans make ny sense???
btw, i got the fact that it is less than one and never 1.
33Should not the answer be 1 (Just as a dil ki awaaz, I have not tried it but a guess)
1i have come up with a very weird solution..
plz dont laugh/
is it something like area = lim a2→4/√3 (√3/4 a2) .....?? where a= side of a triangle.
1i cant think too much.. pls some more hint.. plz... i like this question.. very tough.. but i cant solve :(
1arey dun post it r8 now
PLEEAAAAAAAAAASE
pls give sum more time........ pls.
i saw it jus yesterday.... n have thinking ever since........
let me think a little more....
62u need to draw the triangle of maximum area (among those n points)...
THen add one point with the property that it has lower area than that triagle
So what region will this point fall?
I guess this should be hint enuf.. (actually very close to the solution.. just try!)
U will love the solution.. I will post this solution also today!