Question

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

Answer 1

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 (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.