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)
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(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)
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(Solomon 1978, p. 28), and furthermore
(3)
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(Santaló 1953; Solomon 1978, p. 28).