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

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Solution

Q.
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

1 $5$ cm

2 $5 \sqrt{2}$ cm

3 $2 \sqrt{5}$ cm

4 $10$ cm

Ans.
(2)

PA = PB (Tangents from an external point P)

$∆ APB$ is a Right angle Triangle

$A B^{2} = A P^{2} + P B^{2}$ $[AP = PB]$

$A B^{2} = 2 A P^{2}$

$A B^{2} = 2 \times 5^{2}$

$\Rightarrow A B = 5 \sqrt{2} cm$

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