Let a chord of constant length be slid around a smooth, closed, convex curve 
,
and choose a point on the chord which divides it into segments
of lengths 
and 
.
This point will trace out a new closed curve 
, as illustrated above. Provided certain conditions are met,
the area between 
and 
is given by 
,
as first shown by Holditch in 1858.
The Holditch curve for a circle of radius 
is another circle
which, from the theorem, has radius
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Math. Statist. 43, 41-47, 1996.Wells, D.