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 (see Fig.
).
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
Proof :
BC is a chord of the inner circle and
So, BM = CM .................1
(Perpendicular OM bisect BC)
Similarly,
AD is a chord of the outer circle and
So, AM = DM .................2
(Perpendicular OM bisect AD )
Subtracting 1 from 2, we get
AM-BM = DM - CM