Hi Lorraine.

The distance from the center to a chord would meet the chord in at a right angle right at the midpoint of the chord.

If you draw this, and also draw the radii involved, you can see two distinct right triangles:

So let a = the distance to the 10 inch chord, then 2a is the distance to the 8 inch chord, according to the description.

Now take a look at what pythagoras has to say:

r² = 5² + a² and r² = 4² + (2a)²

Can you solve this system of simultaneous equations for r?

Cheers,
Stephen La Rocque.