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A and B on plane P

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by sanju09 » Wed May 02, 2012 3:18 am
Points A and B on plane P are 5 inches apart. How many points in plane P are 4 inches from point B and more than 4 inches from point A?
(A) 0
(B) 1
(C) 2
(D) 3
(E) more than 3



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by mathbyvemuri » Wed May 02, 2012 11:59 pm
There would be infinite number of points meeting this criteria.
All the points which are at a distance of 4 inches from B lie on a circle with radius 4 inches and centred at 'B'. These points are infinite in number. Out of this set of points, some points are at more than 4 inches from A and the remaining are at less than 4 inches. Which ever the case, the number is definitely "more than 3", leading to answer option "E"
An interesting point here: The number of points which are 4 inches from point B and 1 inch from point A is one and only one. That point sits prettily in between A and B on the line joining them.
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