Question

In the given figure, tangents PA and PB to the circle centred at O, from point P are perpendicular to each other. If PA = 5 cm, then length of AB is equal to ______.

Options

• 5 cm

• `5sqrt2` cm

• `2sqrt5` cm

• 10 cm

Answer 1

In the given figure, tangents PA and PB to the circle centred at O, from point P are perpendicular to each other. If PA = 5 cm, then length of AB is equal to `bbunderline(5sqrt2  "cm")`.

Explanation:

Given

PA = 5 cm

PA ⊥ PB

∠OAP       ...[90°, AP is a tangent]

∠OBP       ...[90°, BP is a tangent] 

So, APBO is square

            or

ΔAPB is a Right angle Triangle

AB² = AP² + PB²           ...[AP = PB]

AB² = 2AP²

AB² = 2 × 5²

⇒ AB = `5sqrt2` cm