Question

PQ and RS are two parallel chords of a circle whose centre is O and radius is 10 cm. If PQ = 16cm and RS = 12 cm. Find the distance between PQ and RS if they lie on the same side of the centre.

• A. 5 cm
• B. 3 cm
• C. 2.5 cm
• D. 2 cm

Answer 1

The correct option is D

2 cm

PQ = 16cm

$\Rightarrow PL=LQ=8cm$ [ the perpendicular from the centre of the circle bisects the chord]

$△OPL$ is a right angled triangle.

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

$={10}^2-8^2$

= 100 - 64 = 36

$\therefore OL=\sqrt{36}=6cm$

RS = 12cm

$\Rightarrow RM=MS=6cm$

Similarly $△ORM$ is a right angled triangle.

Using Pythagoras theorem we get OM = 8 cm

$\therefore$ LM = 8 - 6 = 2 cm

The distance between the two chords is 2 cm