#234. (a). On a circle which circumscribes an \(n\)-sided (regular) polygon \(A_1A_2 \cdots A_n\), a point \(M\) is taken. Prove that the sum of the squares of the distances from this point to all the vertices of the polygon is a number independent of the position of the point \(M\) on the circle, and that this sum is equal to \(2nR^2\), where \(R\) is the radius of the circle.

(b) Prove that the sum of the squares of the distances from an arbitrary point \(M\), taken in the plane of a regular \(n\)-sided polygon \(A_1A_2 \cdots A_n\) to all the vertices of the polygon, depends only on the distance \(l\) of the point \(M\) from the center \(O\) of the polygon, and is equal to \(n(R^2 + l^2)\), where \(R\) is the radius of the circle circumscribing the regular \(n\)-sided polygon.

(c) Prove that statement (b) remains correct even when point \(M\) does not lie in the plane of the \(n\)-sided polygon \(A_1A_2 \cdots A_n\).