Math, asked by ravi7077, 5 months ago

if a line intersects two concentric circles of centre O at points A,B,C and D.then prove that AB=CD

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Answered by Anonymous

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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if a line intersects two concentric circles of centre O at points A,B,C and D.then prove that AB=CD