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Question

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


  1. True
  2. False


Solution

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, AOB=MON=x.

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

Now, consider ΔABO and  ΔMNO.

Note that OA = OM = radius of the circle,

                OB = ON = radius of the circle

and   AOB=MON(=x)

 Therefore by SAS criterion, ΔAOBΔMON.

By CPCT, we have AB = MN.

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