Question

In the following figure , the line ABCD is perpendicular to PQ where P and Q are the centres of the circle show that :(i) AB=CD

Answer 1

In the circle with centre $Q,QO\perp AD$
$\therefore OA=OD...\left(1\right)$
(perpendicular drawn from the centre of a circle to a
chord bisect it)
In the circle with centre $P,PO\perp BC$
$\therefore OB=OC...\left(2\right)$
(perpendicular drawn from the centre of a circle to a
chord bisect it)
$eq.\left(1\right)-\left(2\right)$ gives,
$OA-OB=OD-OC$
$AB=CD$ Proved