Question

If a line intersects two concentric circles with center O at A,B,C and D.prove that AB= CD.​

Answer 1

⠀⠀ ⠀ ⠀⠀ $\huge{\tt{\red{❥}\green{A}\purple{N}\pink{S}\blue{W}\orange{E}\red{R}}}$

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.