Let AB and CD be two diameters of the circle. For an arbitrary point P on the circle, let R and S be the feet of the perpendiculars from P to AB and CD, respectively. Show that the length of RS is independent of the choice of P.

This is really a difficult problem may I ask from where did you pick this question I have to check the booklet because I have been solving this problem for 30 minutes but couldn't find any solution I also checked this problem in my Mathematic course outline which I'm doing from

HCMI but there is no question is there like this one, but I'm trying my best to solve it .