Determining the diameter of a hole within a circle

Hi,

Can someone nudge me in the right direction to solving this problem?

I have a circle with a circular hole in it. I keed to find the diameter of the hole (d)

1. The circle diameter is D

2. The center coordinates of the hole is unknown

3. The hole can be anywhere within the circle

4. The hole is not in the center of the circle

Do you think it is possible to calculate the diameter of the hole by

creating two chords from a fixed coordinate on the circumference of

the circle that run tangental to, and on either side of the hole?

Would it be correct to suggest that

c1 + c2 <= 2D

Where c1 and c2 are the lengths of the two chords

D is the diamater of the circle

Am I on the right track? Where do I go from here?

Any help is appreciated.