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