Question

In the given figure, AB and AC are tangents to a circle with centre O and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is

(a) 9 

(b) 15 

(c) √353 

(d) 25

Answer 1

Correct answer is (b) 15

We know that the radius and tangent are perpendicular at their point of contact 

In right triangle AOB 

By using Pythagoras theorem, we have

OA² = AB² + OB²

\(\Rightarrow\) 17² = AB² + OB²

\(\Rightarrow\) 289 = AB² + 64

\(\Rightarrow\) AB² = 225

\(\Rightarrow\) AB = 15 cm

The tangents drawn from the external point are equal 

Therefore, the length of AC is 15 cm