Question

If the angles subtended by two chords of a circle at the centre are equal, then the lengths of the chords are unequal.

• A. True
• B. False

Answer 1

The correct option is B

False

Let us consider two chords AB and MN of the circle.
It is given that the angles subtended by these chords at the centre is are equal. Say, $\angle AOB=\angle MON=x.$

Let us join the ends of the chords to the centre O.

Now, consider $\Delta$ABO and $\Delta$MNO.

Note that OA = OM = radius of the circle,

OB = ON = radius of the circle

and $\angle AOB=\angle MON(=x^{\circ })$

$\text{Therefore by SAS criterion,}\Delta AOB\cong \Delta MON.$

By CPCT, we have AB = MN.