An equichordal point is a point 
for which all the chords of a curve
passing through 
are of the same length. In other words, 
is an equichordal point if, for every chord ![[x,y]](/images/equations/EquichordalPoint/Inline5.svg)
of length 
of the curve 
, 
satisfies
 |
(1)
|
A function 
satisfying
 |
(2)
|
corresponds to a curve with equichordal point (0, 0) and chord length 
defined by letting 
be the polar equation
of the half-curve for 
and then superimposing the polar equation
over the same range. The curves illustrated above correspond to polar equations of the form
 |
(3)
|
for various values of 
.
Although it long remained an outstanding problem (the equichordal point problem), it is now known that a planar convex region can not have two equichordal points (Rychlik 1997).
