MCQ

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

#### Options

34 cm

15 cm

23 cm

30 cm

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#### Solution

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 `

Is there an error in this question or solution?

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