A circle is drawn on a sphere whose centre is also the centre of the s

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A circle is drawn on a sphere whose centre is also the centre of the sphere. There are 10 circles drawn on the sphere, no three of which meet at any point. How many regions do they divide the sphere?

(a) 142 
(b) 56 
(c) 92 
(d) 320 
(e) 120

srini123 · Answer

do u have a solution for this.. I am feeling very lazy even to start thinking on how to approach this

BarneyStinson · Answer

what is the source of the question? Can somebody explain how the center of a circle drawn on a sphere ( I am classically assuming based on the sentence structure that the circle is drawn on the surface) is the same as the center of the sphere itself? Am I insane in missing something???

Bunuel · Answer

I really doubt that this is a GMAT question.

"A circle is drawn on a sphere whose centre is also the centre of the sphere" - is called great circle, it's an equator of the sphere.

Generally (n+1)th circle adds 2n new regions.

As one circle divides the sphere in 2 regions, two will divide in 4, 3 in 8. For the fourth circle # of regions would be 8+2*3=14. From this you can calculate that 10 great circles divide the sphere in 92 regions.

There is a formula for counting # of regions for n great circles =n^2-n+2. If n=10 --> # of regions=100-10+2=92.

But again it's not GMAT question, so no need to study this.

srini123 · Answer

Great, thanks..
However "There are 10 circles drawn on the sphere,  no three of which meet at any point " how is the bold part play into the question? does it matter at all ?

Bunuel · Answer

Yes, it matters. This means that these circles are not like meridians, as any three meridians meet at two points the north and south poles. If the question were without this part the answer would be different:

One meridian divides the sphere in 2 regions,
Two meridians divide the sphere in 4 regions,
Any additional meridian adds two more regions, hence the general formula would be: # of regions for n meridians=2n.

Hope it's clear.

srini123 · Answer

Thanks Bunuel, that makes it very clear... u r awesome as always

BarneyStinson · Answer

Aaarrrrrgggggghhhhhhhhhhh!!!! My awesomeness again deceived me into not thinking this simple logic. Had been thinking of circles on the surface of the sphere like the cosco or nike symbols on a soccer ball and wondered how could the centers ever be the same!!!!

Definitely, not a GMAT question, but I'dn't recommend not to understand the concept though.

A circle is drawn on a sphere whose centre is also the centre of the s

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