MathDB

Given a circle

k

and the point

P

outside it, an arbitrary line

s

passing through

P

intersects

k

at the points

A

and

B

. Let

M

and

N

be the midpoints of the arcs determined by the points

A

and

B

and let

C

be the point on

AB

such that

PC^2=PA\cdot PB

. Prove that

\angle MCN

doesn't depend on the choice of

s

. [Moderator edit: This problem has also been discussed at http://www.mathlinks.ro/Forum/viewtopic.php?t=56295 .]

Problem Statement