A circle of radius 4 is contained in the plane y=7.

Both circles lie on the surface of a sphere.

What is the radius of the sphere?

Let one of the unknown legs be x, and the other (4-x).  Then

r^2 = 2^2 + (4-x)^2 = 4^2 + x^2

Forgetting r for the moment, and expanding:

20 - 8x + x^2 = 16 + x^2

Solving:

x=1/2

Substituting:

r^2 = 16 + 1/4

r=sqrt(16.25) or about 4.031128874149275.