Geometry Problem

I wish you had provided an OA. However here goes my attempt. Solving this from scratch will be long so following a couple of methods.

My first instinct is (E). Because the radius most likely is a factor of a multiple of 8. so 32/X looks the part. This is purely a guess.

Now some logic:
From the diagram, the diameter of the circle must lie between 8 & 16 ==> radius of the circle must lie between 4 and 8.

Now lets look at each choice. Assume sqrt(5) ~ 2 or 2.2 (to get ranges)

A) less than 1 [NO]
B) <1 [NO]
C) between 1 and 2 [NO]
D) between 2 and 3 [NO]
E) Already choice by process of elimination . But quick calculation also puts value of E between 6 and 7. This is the only choice within the range of 4 and 8 we expected radius to be.

Hence (E)