Calculate Width of Circle?

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Grey Alien

Hi does anyone know how to calculate the Width of circle at different vertical positions. So imagine I wanted to animate a scanning horizontal line down from the top of the circle to the bottom of the circle. At the top the line would not be very wide and in the middle it would be 2*radius, and it would be small again by the bottom.

So how to work the width out for a given Y coord? Any ideas? Thx :-)