Question

If the two chords in a circle are equal, then the angles they subtend at the centre are the same.

• A. True
• B. False

Answer 1

The correct option is A True

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

Now, let us join the ends of the chords to the Centre of the circle.

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

OA = OP = r , where r is the radius of the circle .

Also,
OB = OQ = r , and

AB = PQ (given).

$\therefore \Delta AOB\cong \Delta POQ$ by SSS criterion.

Therefore, by C.P.C.T., $\angle AOB=\angle POQ.$

Therefore, equal chords subtend equal angles at the centre of the circle.