Question

In a figure, If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D. Prove that AB = CD

Answer 1

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

To prove : AB = CD

Construction : Draw OM $\perp$ BC.

Proof: The perpendicular drawn from the centre of a circle to a chord bisects the chord.
AM = DM ---(1)
BM = CM -----(2)
Subtracting (2) from (1), we get
AM - BM = DM - CM
$\Rightarrow$ AB = CD

Hence Proved