Circle Chords of a Specific Length

I've searched high and low for a solution to this one, with no luck.  I want to calculate the ending point of a chord given a specific pixel length.

I have the center point of the circle, the radius, and a point (x,y in the illustration) on the circle.  I want the ending point (?,?) of a line a specific number of pixels away from x,y.

Something like...

function PointF GetChordPoint(PointF center, float radius, PointF start, float length)