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

(a) 8cm 

(b) 14 cm 

(c) 16 cm 

(d) √136 cm

Answer 1

Correct answer is (c) 16 cm

We know that the radius and tangent are perpendicular at their point of contact In right triangle AOP

AO² = OP² + PA²

\(\Rightarrow\) 10² = 6² + PA²

\(\Rightarrow\) PA² = 64

\(\Rightarrow\) PA = 8 cm

Since, the perpendicular drawn from the center bisect the chord

∴ PA = PB = 8 cm

Now, AB = AP + PB = 8 + 8 = 16 cm