Question

In the given figure, O is the centre of two concentric circles of radii 6 cm and 10 cm. AB is a chord of outer circle which touches the inner circle. The length of chord AB is ______.

Options

• 8 cm

• 14 cm

• 16 cm

• `sqrt(136)` cm

Answer 1

In the given figure, O is the centre of two concentric circles of radii 6 cm and 10 cm. AB is a chord of outer circle which touches the inner circle. The length of chord AB is 16 cm.

Explanation:

Let O be the common centre and P the point of contact.

OP ⟂ AB, so P is the midpoint of chord AB.

Let AP = x.

In right triangle OAP,

OA = 10 and OP = 6,

So x = AP = `sqrt(OA^2 - OP^2)`

= `sqrt(100 - 36)`

= 8

Hence AB = 2·AP

= 16 cm