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 Fig. 10.25).

Question

Philoid · Accepted Answer

Let us draw a perpendicular OM on line AD

It can be observed that BC is the chord of the smaller circle and AD is the chord of the bigger circle

We know that perpendicular drawn from the centre of the circle bisects the chord

BM = MC (i) And,

AM = MD (ii)

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

AM − BM = MD − MC

AB = CD