Consider a convex plane curve 
with perimeter 
, and the set of points 
exterior to 
. Further, let 
and 
be the perpendicular distances from 
to 
(with corresponding tangent points 
and 
on 
), and let 
. Then
 |
(1)
|
(Crofton 1885; Solomon 1978, p. 28).
If 
has a continuous radius of curvature and the
radii of curvature at points 
and 
are 
and 
, then
 |
(2)
|
(Solomon 1978, p. 28), and furthermore
 |
(3)
|
(Santaló 1953; Solomon 1978, p. 28).
