Blue line => $ L/2 = \sqrt{R^2-D^2} $
Length $ = 2*(L/2)=2*\sqrt{R^2-D^2} $
let X be the length of chord
$ X=2*\sqrt{R^2-D^2} $ if $ 0<D<R \,\ $
$ X=2*R \,\ $ if $ D=0 \,\ $
$ X=0 \,\ $ else
so its PDF will be $ \int_0^{2*R} \sqrt{R^2-D^2} $
