Question

O is the centre of the circle and AB is parallel to CD.AB=24cm and distance between the chords AB and CD is 17cm. If the radius of the circle is 13cm find the length of the chord CD​

Answer 1

The length of chord CD is 10 cm.

1. From the figure AB is a chord and O is center of circle. Dropping a perpendicular from O on to AB divides the AB into two halves.

Considering right angled triangle AMO

AO²=AM²+OM²

OM²=AO²-OM²=13²-12²=169-144=25

OM=5 cm

2. Given MN=17 cm so ON must be 17-5=12cm

3. Now consider right angled triangle ONC

OC²=ON²+NC²

NC²=OC²-ON²=13²-12²=169-144=25

NC=5 cm

CD=2*NC

CD=10cm

The length of chord CD is 10 cm.

Answer 2

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