Question

If the line intersects two concentric circles with the same centre with centre O at A,B,C and D prove that AB=BC?​

Answer 1

*Answer:

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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. ✓

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