Question

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 (see figure)

Answer 1

Construction : Draw $OP\perp AD$
For outer circle, AD is chord
$\therefore AP=PD...\left(1\right)$
(Perpendicular from centre bisect the chord & for inner circle, BC is chord)
$\therefore BP=PC....\left(2\right)$ (Perpendicular from centre bisect the chord)
Subtract equation (2) from equation (1)
$\Rightarrow AP–BP=PD–PC\Rightarrow AB=CD$