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
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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