Question

A line p, meets two concentric circles , with same centre O, at A, B, C and D as shown in the figure .prove that triangle OAB congruent triangleODC.
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Answer 1

Answer:

Step-by-step explanation:

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.