# Q: 4    If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that $\small AB=CD$ (see Fig. $\small 10.25$).

S seema garhwal

Given: a line intersects two concentric circles (circles with the same centre) with centre O at A, B,  C and D.

To prove : AB  = CD

Construction: Draw $OM\perp AD$

Proof :

BC is a chord of the inner circle and $OM\perp BC$

So, BM = CM  .................1

(Perpendicular OM bisect BC)

Similarly,

AD  is a chord of the outer circle and $OM\perp AD$

So, AM = DM  .................2

Subtracting   1 from  2, we get

AM-BM = DM - CM

$\Rightarrow AB = CD$

Exams
Articles
Questions