Question

In the given figure, l is a line intersecting the two concentric circles, whose common center is O, at the points A, B, C, and D. Show that AB = CD.

Answer 1

Let OM be perpendicular from O on line l.
We know that the perpendicular from the centre of a circle to as chord; bisect the chord.
Since BC is a chord of the smaller circle and OM ⊥ BC.
∴ BM = CM                 ....(i)
Again, AD is a chord of the larger circle and OM ⊥ AD.
∴ AM = DM                 ....(ii)
Subtracting (i) from (ii), we get,
AM - BM = DM - CM ⇒ AB = CD
Hence proved.