Question

Two concentric circles of radii 5 cm and 3 cm are drawn. Find the length of the chord of the larger circle which touches the smaller circle.

Answer 1

Given: Two circles of radii 3 cm and 5 cm with common centre.

Let AB be a tangent to the inner/small circle and chord to the larger circle. 

Let ‘P’ be the point of contact. 

Construction: Join OP and OB. 

In △OPB ; 

∠OPB = 90°

 [radius is perpendicular to the tangent] 

OP = 3cm OB = 5 cm 

Now, OB² = OP² + PB² 

[hypotenuse² = Adj. side² + Opp. side² , Pythagoras theorem]

5² = 3² + PB² 

PB² = 25 – 9 = 16 

∴ PB = √16 = 4cm. 

Now, AB = 2 × PB 

[∵ The perpendicular drawn from the centre of the circle to a chord, bisects it] 

AB = 2 × 4 = 8 cm. 

∴ The length of the chord of the larger circle which touches the smaller circle is 8 cm.