MathDB

1-Let

A

and

B

be two diametrically opposite points on a circle with radius

1

. Points

P_1,P_2,...,P_n

are arbitrarily chosen on the circle. Let a and b be the geometric means of the distances of

P_1,P_2,...,P_n

from

A

and

B

, respectively. Show that at least one of the numbers

a

and

b

does not exceed

\sqrt{2}

1