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geometry need expert help

by quantskillsgmat » Sun Dec 25, 2011 2:35 am
There is circle of radius 1 unit. each member of a sequence of regular polygon S1(n),n=4,5,6.... where n is number of sides of the polygon, is circumscribing the circle and each member of sequence of regular polygon S2(n), n=4,5,6,... where n is number of sides of polygon,is inscribed in circle.Let L1(n)and L2(n) denote perimeter of corresponding polygon of S1(n) and S2(n).then (L1(13)+6.28)/L2(17) is
a)greater than 3.14/4
b)between 1 and 2
c)greater than 2
d)less than 3.14/4
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by user123321 » Sun Dec 25, 2011 6:23 am
quantskillsgmat wrote:There is circle of radius 1 unit. each member of a sequence of regular polygon S1(n),n=4,5,6.... where n is number of sides of the polygon, is circumscribing the circle and each member of sequence of regular polygon S2(n), n=4,5,6,... where n is number of sides of polygon,is inscribed in circle.Let L1(n)and L2(n) denote perimeter of corresponding polygon of S1(n) and S2(n).then (L1(13)+6.28)/L2(17) is
a)greater than 3.14/4
b)between 1 and 2
c)greater than 2
d)less than 3.14/4
IMO C
I think you are asking for (S1(13)+6.28)/S2(17))

one good thing is always inscribed polygon has less length than circumscribed polygon whatever maybe the number of sides it is having.
so S1(13)/s2(17) > 1

perimeter of given circle = 2*pi = 6.28
so 6.28/S2(17) will be atleast 2 since S2(17) can have a max of 2*pi
=> 6.28/S2(17) > 2

so on the whole (S1(13)+6.28)/S2(17)) > 1+2

user123321
Just started my preparation :D
Want to do it right the first time.
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