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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
Options
34 cm
15 cm
23 cm
30 cm
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 `
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