" (i) "(2-sqrt(3))/(sqrt(3))

Three equal circles each of radius r touch one another. The radius of the circle touching all the three given circles internally is (a) (2+sqrt(3))r (b) ((2+sqrt(3)))/(sqrt(3))r (c) ((2-sqrt(3)))/(sqrt(3))r (d) (2-sqrt(3))r

(1+2sqrt(3))/(2-sqrt(3))

(2+sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))+(sqrt(3)+1)/(sqrt(3)-1)is

(2+sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))=

((2+sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))+(sqrt(3)-1)/(sqrt(3)+1)) simplifies to 16-sqrt(3)(b)4-sqrt(3)(c)2-sqrt(3) (d) 2+sqrt(3)

(2 - sqrt3)/sqrt3

(5+sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))

If sqrt(2) = 1.414, sqrt(3) = 1.732, sqrt(5) = 2.236 and sqrt(6) = 2.449 , find the value of (2+sqrt(3))/(2-sqrt(3)) +(2-sqrt(3))/(2+sqrt(3)) +(sqrt(3) -1)/(sqrt(3) +1)