Question

PQ and RS are two parallel chords of a circle whose centre is O and radius is 5 cm. If PQ = 8 cm and RS = 6 cm.The distance between PQ and RS if they lie on the same side of the centre is ___ cm

Answer 1

PQ = 8cm

$\Rightarrow PL=LQ=4cm$ [ the perpendicular from the centre of the circle bisects the chord]

$△OPL$ is a right angled triangle.

$\therefore O{L}^2=O{P}^2-P{L}^2$

$=5^2-4^2$

= 25 - 16 = 9

$\therefore OL=\sqrt{9}=3cm$

RS = 6cm

$\Rightarrow RM=MS=3cm$

Similarly $△ORM$ is a right angled triangle.

Using Pythagoras theorem we get OM = 4 cm

$\therefore$ LM = 4 - 3 = 1 cm

The distance between the two chords is 1 cm