Question

A chord of length 14 cm is at  a distance of 6 cm from the centre of a circle. The length of another chord at a distance of 2 cm from the centre of the circle is

विकल्प

•  12 cm

•  12 cm

•  12 cm

• 18 cm

Answer 1

18 cm

We are given the chord of length 14 cm and perpendicular distance from the centre to the chord is 6 cm. We are asked to find the length of another chord at a distance of 2 cm from the centre.

We have the following figure

We are given AB = 14 cm, OD = 6 cm, MO = 2 cm, PQ = ?

Since, perpendicular from centre to the chord divide the chord into two equal parts

Therefore

`AQ^2 = AD^2 +OD^2`

          = ` 7^2 + 6^2`

          = 49 + 36

        `= sqrt( 85)`

Now consider the ΔOPQ in which OM = 2 cm

So using Pythagoras Theorem in ΔOPM

`PM^2 = OP^2 -OM^2`

  `=(sqrt(85))^2 - 2^2`         (∵ OP = AO = radius) 

   = 81 

  = 9 cm 

Hence PQ = 2 PM 

                 = 2 × 9 

                 = 18 cm