Question

the length of each of two parallel chords is 16 cm. If the length of the radius of the circle is 10 cm , then what is the distance between two chords ?
options :- (i) 12 cm
(ii) 16 cm
(iii) 20 cm
(iv) 5 cm​

Answer 1

Step-by-step explanation:

Diagram:- Refer the attachment

Solution:-

Let AB and CD be the chords of the circle.

⇢ AB = CD = 16cm

And O be the centre of the circle.

Draw PQ ⊥ AB. Join OD and OB such that OD and OB are the radii of the circle.

⇢ OD = OB = 10cm $\: \: \:\:\:\:$ [ Radii ]

⇢ PD = ½ × CD = 8cm

⇢ QB = ½ × AB = 8cm

In △ POD, ∠OPD = 90°

By Pythagoras Theorem:-

$\rm \dashrightarrow OD^{2} = PD^{2} + OP^{2}$

$\rm \dashrightarrow OP^{2} = OD^{2} - PD^{2}$

$\rm \dashrightarrow OP^{2} = 10^{2} - 8^{2}$

$\rm \dashrightarrow OP = \sqrt{100 - 64}$

$\rm \dashrightarrow OP = \sqrt{36} = 6cm$

Similarly, OQ = 6cm

⇢ PQ = OP + OQ

⇢ PQ = 6 + 6

⇢ PQ = 12cm

$\underline{\boxed{\therefore \rm The \: distance \: between \: two \: chords = 12cm}}$

$\rm \underline{ Option \: (i) \: is \: correct}$