geometry

[sud21]

In a given square T we inscribe a circle S. Into that circle we inscribe a square R. Is the circumference of S greater than 10?
1). The side of square R is greater than 2
2). The side of square T is greater then 4


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[neelgandham]

Let the side of square R be a, then
The radius of circle S = a/√2 and
The side of square T = √2*a

So, the question can be rephrased to Is pi*a*√2 > 10?

1). The side of square R is greater than 2

Given a > 2 then pi*a*√2 > pi*2*√2(~8.8). Insufficient to answer the question as
pi*a*√2 > 8.8 doesn't mean that pi*a*√2 > 10.

2). The side of square T is greater then 4

Given √2*a > 4 (a > 2√2),then pi*a*√2 > pi*2√2*√2, i.e pi*a*√2 > ~12.5. Sufficient to answer the question Is pi*a*√2 > 10?

IMO B