Question

If a line / lintersects two concentric circles (each with centre O)
at the points A, B, C and D as shown in the adjoining figure,
prove that AB = CD.
Hint. Draw OEIL​

Answer 1

Answer:

We know that, OA=OD and OB=OC.  

They are radius of respective circles.

In ΔOBC, we know that OB=OC, so ∠OBC=∠OCB

∴∠OCD=∠OBA

In ΔOAD, we know that OA=OD, so ∠OAD=∠ODA

Since, ∠OCD=∠OBA and ∠OAD=∠ODA, we get ∠AOB in ΔOAB is equal to ∠COD in ΔOCD.

∴ From SAS congruency, we can say that ΔOAB and ΔOCD are congruent.

So, AB=CD.

Step-by-step explanation: