Question

In a circle of radius 17 cm, two parallel chords are drawn on opposite side of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is

पर्याय

• 34 cm

• 15 cm

• 23 cm

• 30 cm

Answer 1

30 cm 

Given that: Radius of the circle is 17 cm, distance between two parallel chords AB and CD is 23 cm, where AB= 16 cm. We have to find the length of CD.

We know that the perpendicular drawn from the centre of the circle to any chord divides it into two equal parts.

So, AM = MB = 8 cm

Let OM = x cm

In triangle OMB,

`x = sqrt(17^2 - 8^2 = 15)`

Now, in triangle OND, ON = (23 − x) cm = (23 − 15) cm = 8 cm

`ND = sqrt(OD^2 -ON^2)`

`⇒ ND = sqrt(17^2 - 8^2 = 15)`

Therefore, the length of the other chord is

`CD = 2 xx 15 = 30   cm `