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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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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