Subcontests
(4)independent sum of squares involving two concentric circles
Let C1,C2 be two distinct concentric circles, and BA be a diameter of C1. Choose the points M,N on C1,C2, respectively, but not on the line BA.
a) Show that there are unique points P,Q on MA,MB, respectively, so that N is the middle of PQ.
b) Prove that the value AP2+BQ2 does not depend on M,N.Mihai Piticari, Mihail Bălună