Need to find radius, knowing only chord length and arc height?

I have a rectangle 8 units wide and 1 unit tall. I want to inscribe an arc from a circle that intersects both left and right lower corners and the mid-point of the upper horizontal line. So - the chord length is 8, the highest point of the arc above the chord is 1 (what is the name of this line?), what is the radius of the circle. I know intuitively that there is one and only one circle that does this, but I can't remember enough trig to figure it out in a timely manner. THANKS!