91Ó°ÊÓ

(a) Prove that the perpendicular bisector of a chord of a circle is diameter. (b) Given a circle, how would you construct the center?

(a) Given concentric circles, prove that two chords of the larger circle that are tangent to the smaller circle are congruent. (b) Given a circle with center \(C,\) a point \(P,\) and length \(d,\) construct a line through \(P\) such that the length of the chord is \(d\)

Use the solution of Queen Dido's problem to prove the following: Of all the regions with a given perimeter, the circle has the greatest area. [Hint: Let \(A\) and \(B \text { be points on the boundary which divide the perimeter in half. }]\)