85 Pentagon incribed in circle

1.Question is "A pentagon" and NOT "a regular pentagon" so there is no scope of calculating central angle and using it with radius to determine the side of a pentagon. SO NOT SUFFICIENT.

2.Diagonal is less than 8..say 7 but there is no way we can find the sides.So NOT SUFFICIENT

Taking 1 and 2 we have a triangle with two sides 4 and third side less than 8, which is impossible as it should be greater than 8.So NOT SUFFICIENT


So Answer should be E

Pardon me! I forgot to mention that it is a regular Pentagon

IMO A.

From statement 1, we know that the radius of the circle is 4.

Circumference of the circle is 8*pi

You can draw 5 triangles from the center of the circle. If its a regular pentagon, a single angle in the center is 360/5=72.

We know the circumference of the circle and we know one angle of a triangle from the center.

Find the length of 72 angle arc.

ie, 360/8*pi=x/72;

You'll get 5.024 as the length of the arc.

If the arc itself is only 5, then the chord(ie, one of the pentagon) will be less than that. So, the perimeter of the pentagon will be less than 25.

We can't find anything through the statement 2. So, its not sufficient.

OA pls.