Question

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:

Options

• 16 cm

• 10 cm

• 14 cm

• 20 cm

Answer 1

16 cm

Explanation:

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.