Sphere Cut by Parallel Planes

[YummyNoodles]

The problem: A sphere is cut by two parallel planes that are 6 units apart. These planes intersect the sphere in diameter 5 and 7 respectively. Compute the radius of the sphere.

I have collapsed the sphere into a circle with two chords measuring 5 and 7, like my teacher suggested (see attached image). However, I'm not sure how to go from there. It feels like there is not enough information to complete the problem. Please help!

 

[Cubist]

Do the added triangles CAB and CDE (see image below) give you any ideas?

 

[YummyNoodles]

Do the added triangles CAB and CDE (see image below) give you any ideas?

View attachment 18103

I used your drawing to compute x but found a negative value. I then used that value of x to find the radius, sqrt(18.5). Would this be correct?

 

[lev888]

Negative x indicates that the lower plane is below the center of the sphere.