The Total solution for NCERT class 6-12
4. If a line intersects two concentric circles (circles with the samecentre) with centre O at A, B, C and D, prove that AB = CD (see Fig. 10.25).
The given image is asfollows:
First, draw a linesegment from O to AD such that OM ⊥ AD.
So, now OM isbisecting AD since OM ⊥ AD.
Therefore, AM = MD —(i)
Also, since OM ⊥ BC, OM bisects BC.
Therefore, BM = MC —(ii)
From equation (i) andequation (ii),
AM-BM = MD-MC
∴ AB = CD