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Vivek Balakrishnan Grade: 11
```        ABCD is a square. The midpoints of the sides are joined to form a square A1,B1,C1,D1. The same way we form another square A2,B2,C2,D2 from A1,B1,C1,D1. This process of forming squares is continued.
Question:
The ratio of the areas of the circum circle and area of the square is ?
A. Depends on the radius of the circle.
B. Independent of the radius of circle.

If A why ? If B why?```
7 years ago

419 Points
```										Dear Vivek
Question is not clear.i.e. ratio of which circumcircle and which square beacause as mentioned in the question there are many squares ABCD,A1B1C1D1, A2B2C2D2..etc.
All the best.
AKASH GOYAL

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```
7 years ago
510 Points
```										let the side of outermost square is a....
after drawing the diagram it is clear that  radius of circumcircle is 1/21/2 times the side of square ....
side of inner square is 1/21/2 times side of outer square.....
now if the side of outermost square is a then we have
a1,a2,a3,a4.......        =     a        ,   a/21/2 ,       a/2   ,       a/2.21/2  and so on...
r1,r2,r3,r4........         = a/21/2   ,      a/2    ,      a/2.21/2  ,     a/4  and so on
now
area's of circumcircle is ,
Ac = pi(r12 + r22 + r32  ............infinity)
=(pi)a2 (1/2 +1/4 +1/8 +1/16 .....infinity)                    (sum of infinite GP is a/a-r)
=(pi)a2 ............1
area's of square is ,
As =a2 (1 + 1/2 + 1/4 + 1/8 ...........infinity)
As = 2a2 ...............2
dividing 1 and 2
eq1/eq2=pi/2            independent of radius of circle...
hence option B is correct
```
7 years ago
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