Question

AB and CD are two parallel chords of length 24 cm each of a circle of a circle of diameter PQ of 26 cm. Find the distance between the two chords.
1. 12 cm 
2. 10 cm
3. 13 cm
4. 14 cm

Answer 1

Correct Answer - Option 2 : 10 cm

Given∶

AB and CD are of length 24 cm each.

Diameter of a circle 26 cm.

Formula Used∶

Theorem "Perpendicular drawn from the centre to a chord of a circle, bisect the chord."

Pythagoras theorem.

Calculation∶

AB = CD = 24 cm

OP ⊥ AB

So, 1/2 AB = AP = BP - [Perpendicular drawn from the centre to a chord of a circle, bisect the chord]

AP = 1/2 × 24 = 12 cm

Also, OB = OQ

Diameter = 26 cm

Radius = Diameter/2 = 26/2 = 13 cm

OA = 13 cm

In ΔOAP

OP² = OA² - AP²      [Pythagoras theorem]

⇒ OP² = 13² - 12²

⇒ OP² = 169 - 144

⇒ OP² = 25

⇒ OP = 5 cm

So, QP = 2 × OP = 2 × 5 = 10 cm

∴ The distance between QP is of 10 cm.