Question

In the given figure, O is the centre of two concentric circles of radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm then PB is equal to ______.

Options

• `5sqrt(2)` cm

• `3sqrt(5)` cm

• `4sqrt(10)` cm

• `5sqrt(10)` cm

Answer 1

In the given figure, O is the centre of two concentric circles of radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm then PB is equal to `underlinebb(4sqrt(10)  cm)`.

Explanation:

Join OB. Then, OA = 5 cm, OB = 3 cm.

`OP = sqrt(OA^2 + PA^2)`

= `sqrt(5^2 + 12^2)`

= 13 cm

`PB = sqrt(OP^2 - OB^2)`

= `sqrt(13^2 - 3^2)`

= `sqrt(160)  cm`

= `4sqrt(10)  cm`