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

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

1. A
34cm
2. B
15 cm
3. C
23 cm
4. D
30cm

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### Solution:

It is given that the radius of circle is 17cm.
And two parallel chords at a distance of 23cm between them, drawn on opposite sides of the diameter.
Let the diameter cut the chords AB and FD at points E and C respectively.
Let radius OA=17cm, EC=23cm and AB=16cm.
We know that the perpendicular from the center to the chord bisects the chord.
and AE=EB=8cm.
In  ,
By Pythagoras theorem,

Now, OC = CE – OE.
OC = 23 – 15
OC = 8cm.
In ΔOCD,
By Pythagoras theorem,
We know that the perpendicular from the center to the chord bisects the chord.

Therefore, the correct option is (4).

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