In a circle of radius 5cm,PQ and RS are two chords of lengths 8cm and 6 cm respectively. Calculate the distance between the chords, if they are on:

i)  the same side of the centre.

ii)  Opposite sides  of the centre.

(1)

Given: PQ = 8 cm, RS = 6 cm and radius of the circle = 5 cm

∴ OS = OQ = 5 cm

Now we know that perpendicular from the centre of the circle to the chord bisects the chord.

In right Δ OBS

OS² = OB² + BS²                (Pythagoras theorem)

⇒  OB² = OS² – BS² = 5² – 3² – 25 – 9 = 16 cm² 

In right Δ OAQ

OQ² = OA² + AQ² 

⇒  OA² = OQ² – AQ² = 5² – 4²  =  25 – 16 = 9 cm²

Hence distance between the chords = OB – OA = 4 cm – 3 cm = 1 cm

(2)

Hence distance between the chords = OA + OB

= 4 cm + 3 cm = 7 cm