Circles: Center and Radius!

Suppose we have a circle and we take off a random portion. We don't know how much we took off but we do know we took it off at the top of the circle. The measure of our newly formed "semi circle" is 32 inches across, and 6 inches in height. How would I go about finding the center and radius of the complete circle. Picture included to those whom I might have confused.



Gracias.

Well, if it's a semi-circle, then 32 divided by 2 is your radius. (16)

I have no clue about the center.

what if the base of the semi-circle is not the full diameter of the original circle? Then the radius might be something totally different than your answer.

Sorry, just spotted an error that might mess you up. I have no clue about the actual question, since I forgot (funny how that happens over summer vacation, no?).

If this is a construction problem then do the following:

1. Construct the perpendicular bisector of that chord.
2. Draw a second chord on that arc.
3. Construct the perpendicular bisect of the new chord.

The point of intersection of both bisectors is the center.

The a segment connecting the center of a circle to the midpoint of a chord is always perpendicular to the chord.