Q. 11 A14.0( 5 Votes )

# A tangent drawn to a circle with centre O from an external point A touches the circle at the point B. If OB = 5cm, AO = 13cm, then the length of AB is

A. 12 cm

B. 13cm

C. 6.5 cm

D. 6 cm

Answer :

The ΔABO formed by joining the three points is always a right angled triangle

AO is the hypotenuse of Δ ABO

Applying Pythagoras theorem :

AB^{2} = AO^{2}-OB^{2}

⇒ AB^{2} = 13^{2}-5^{2}

⇒ AB^{2} = 169-25

⇒ AB^{2} = 144

⇒ AB = 12 cm.

So Correct Option is (A)

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