Question

a line l intersecting two concurrent circles having same Centre is o at the point A,B,C,D show that AB = CD​

Answer 1

Answer:

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(since exterior angles)

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.