Question

Please have a look at this geometry question. In the mean time, I am posting my attempt.

Answer 1

http://gyazo.com/cb97188aea63e902b7547862885ac945

Answer 2

a= 1/2^n
b=1/2^(n+1)

we have to solve for x

Answer 3

OA = a+x
OB=b+x
AB=a+b

DO= sqrt((a+x)^2 - (a-x)^2) = 2sqrt(ax)
and same way
OC = 2sqrt(bx))
Now, AB^2 = OA^2 + OB^2 - 2OA.OB cos(<BOA>)
=> (a+b)^2 = (a+x)^2 + (b+x)^2 + 2(a+x)(b+x)cos<DOA + COB>
=> (a+b)^2 = (a+x)^2 + (b+x)^2 + 2(a+x)(b+x) [ cosDOA cosCOB - sinDOA sinCOB ]

=> (a+b)^2 = (a+x)^2 + (b+x)^2 + 2(a+x)(b+x) [ 2sqrt(ax)/(a+x) . 2sqrt(bx)/(b+x) - (a-x).(b-x)/(a+x)(b+x) ]

Is everything right so far?

Answer 4

oh, seems like I got my mistake! :O