if a line intersect two concentric circles (circles with same centre) with centre O at A,B,C and D prove that AB =

December 2023 1 6 Report

if a line intersect two concentric circles (circles with same centre) with centre O at A,B,C and D prove that AB = CD (see the adjoining figure).

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.