Given a unit square ABCD construct 4 circles centered at each corner and having diagonal radius. Form the smallest of the squares defined by the points where these circles intersect.

Use this process on the new square to create a third square.

1. Find and provide the area [in

**surd**format] of

__each__square so formed.

2. Following this process find a general expression for the area of the n

^{th}square.