Question

if a line intersect two concentric circles ( circles with the same centre) with centre O at A, B, C and D. prove that AB= CD
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Answer 1

OM ⊥ AD is drawn from O.

OM bisects AD as OM ⊥ AD.

⇒ AM = MD --- (i)

also, OM bisects BC as OM ⊥ BC.

⇒ BM = MC --- (ii)

From (i) and (ii),

AM - BM = MD - MC

⇒ AB = CD

Answer 2

Answer:

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

We know that, OA=OD and OB=OC. .In ΔOBC, we know that OB=OC, so ∠OBC=∠OCB

Then, ∠OCD=∠OBA

∠OCD=∠OBAIn 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.

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

Hope it helps you ✌✌