Question

If a line intersect two concentric circle (circle with the same centre) O at A, B, Cand D. prove that AB = CD. ​

Answer 1

Answer:

ANSWER

We know that, OA=OD and OB=OC.

We know that, OA=OD and OB=OC. They are radius of respective circles.

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

n ΔOBC, we know that OB=OC, so ∠OBC=∠OCB∴∠OCD=∠OBA

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

In ΔOAD, we know that OA=OD, so ∠OAD=∠ODASince, ∠OCD=∠OBA and ∠OAD=∠ODA, we get ∠AOB in ΔOAB is equal to ∠COD in ΔOCD.

In ΔOAD, we know that OA=OD, so ∠OAD=∠ODASince, ∠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 (by CPCT).