In the given figure, APB is tangent to the inner circle and also a chord of outer circle. Both the circles are concentric. If OA = 10 cm and OP = 6 cm, the length of AB is :

1. 16 cm

2. 10 cm

3. 14 cm

4. 20 cm

We know that,

Tangent at any point of a circle and the radius through this point are perpendicular to each other.

∴ OP ⊥ AP

In right angle triangle OAP,

By pythagoras theorem,

⇒ OA² = OP² + AP²

⇒ 10² = 6² + AP²

⇒ 100 = 36 + AP²

⇒ AP² = 100 - 36

⇒ AP² = 64

⇒ AP = $\sqrt{64}$ = 8 cm.

Since, AB is the chord to the bigger circle, with center O.

We know that,

Perpendicular from center to the chord, bisects it.

∴ PB = AP = 8 cm.

AB = AP + PB = 8 + 8 = 16 cm.

Hence, Option 1 is the correct option.