Chords KN and ST are perpendicular to diameter CP of circle (O) at points Q and R. SQ intersects the circle in V. (K, S are on one side of CP, N and T on the other.) Let r be the radius of the circle (M) inscribed into the curvilinear triangle TQV. Prove that
1/r = 1/PQ + 1/QR.
In addition, it would be nice to have a short independent proof of the fact that r is independent of the radius of (O).