IMO D

pls post the OA

OA is D but how did you get that?

Let me try.

First, draw lines from the center of pentagon ( and a circle) to its vertices. The lines you draw are equal to radius of the circle a pentagon inscribed in. We have 5 equal triangles now.
the angle between every radius is 360/5=72. Sum of other two angles of every triangle are (180-72)=108. Since every triangle has 2 equal sides, such triangle is isosceles. Hence, the angles of a triangle are 72, 54, 54. Note that the angle of 72 degrees is opposite to the side a pentagon.
We only need to know if the perimeter of a pentagon is >26. So, knowing the relationship among 3 sides of a triangle ( 2 of which are radiuse) we could know the range of a third side of a triangle ) or a side of a pentagon)

(1) given that radius=4
So the side of a triangle (x) must be: x<8 (4+4), 4+x>4=>x>0, and also must be larger than 2 other sides of a triangle (since it has the opposite angle larger)==> x>4, so X:(4;8), the least possible perimeter might be 4.1*5, 5*5=25, 5*6=30. 20,5<26, 25<26, 30>26. Insufficient.

(2) diagonal <8. (really need to have a picture)
When you draw whatever diagonal of our regular pentagon you get a isosceles triangle as well, following the same rules as in the (1) we could get a range of a sides - since the angle of 108 degrees is opposite to the diagonal ==> diagonal of a pentagon is the largest side of a triangle. diagonal is <8. then 2x>8, x>4. and x+8>x, x>0.
If I have not forgotten something. It seems to me like the answer is E. But i clearly don't remember some properties of the regular pentagon. hehe
Good DS question. If someone could remind what am i missing i ll be really pleased )))

on Xam day either i would have wasted my precious time in solving this or would have picked a wrong one under time pressure.the solution is not full proof. its basically understanding the property.

any thing inscribed in a circle will have all the properties sp. perimeter and area less then that of circle.

statement1) radius=4 ; perimeter of circle=2pir=approx 25.12
as the pentagon is inscribed in it perimeter of pentagon will be < 25.12

hence suff

statment2) longest diagonal of penta will be equal to the dia of circle , therefore dia will be < 8
hence perimeter of circle < 25.12, for the same reason perimeter of pentagon<25.12

suff