A kinematic formula for affine diameters and affine medians of a convex set

For a planar convex set $K$ with $C^2$-smooth boundary, the area of the set of the points lying on a given number of affine diameters of $K$ is estimated. As a corollary, it is proved that the area of $K$ is at most $\pi M^2/4$, where $M$ is the largest length of a chord of $K$ halving the area of $K$.