Question

if a line intersect two concentric circles, with center O at A,B,C andD prove that AB=CD ​

Answer 1

Given : A line intersects two concentric circles with centre 0 at A, B, C and D.

To Prove: AB = CD.

Construction: Draw OM⊥BC.

Proof :The perpendicular drawn from the centre of a circle to a chord bisects the chord.

Therefore ,

AM = DM............(1)

BM = CM ...............(2)

Subtracting (2) from (1), we get

AM- BM = DM - CM

AB = CD.

Proven :)