Question

If the two chords in a circle are equal, then the angle it subtends at the centre is same.

• A. True
• B. False

Answer 1

The correct option is A True

Equal chords subtend equal angles at the centre of the circle.

Let us consider two chords AB and PQ which are of equal length.

Now, Join the ends of the chords to the centre of the circle.

In $\Delta$AOB and $\Delta$POQ,

OA = OP = r (radius of the circle)

Similarly,

OB = OQ = r (radius of the circle)

and, AB = PQ (Given in the statement)

$\therefore$$\Delta$AOB $\cong$ $\Delta$POQ

$\therefore$By C.P.C.T., $\angle$AOB = $\angle$POQ.

$\therefore$We can say that the angle subtended by equal chords at the centre is equal.