Question

In the adjoining figure, a tangent is drawn to a circle of radius 4 cm and centre C, at the point S. Find the length of the tangent ST, if CT = 10 cm.

Options

• `sqrt(21)` cm

• `3sqrt(21)` cm

• `2sqrt(21)` cm

• `4sqrt(21)` cm

Answer 1

`2sqrt(21)` cm

Explanation:

The line from the centre to the tangent is perpendicular to the tangent.

∴ CS ⊥ ST

So, in right angled ΔCST, by the Pythagoras theorem,

CT² = CS² + ST²

(10)² = (4)² + ST²

ST² = 100 – 16 = 84

⇒ ST = `2sqrt(21)`

Thus, the length of ST is `2sqrt(21)` cm.