4. If a line intersects two concentric circles (circles with the same centre) with centre
O at A, B, C and D. prove that AB = CD (see figure).

Let OP be the perpendicular from O on linel . Since, the perpendicular from the centre
of a circle to a chord bisects the chords.

Now, BC is the chord of the smaller circle and \(OP\perp{BC}\).

Therefore, BC = PC ...(i)

Since, AD is a chord of the larger circle and \(OP\perp{AD}\).

Therefore, AP = PD ...(ii)

On subtracting Eq. (i) from Eq.(ii), we get,

AP - BP = PD - PC

Thus, AB = CD

Hence, it is proved.