Q. 64.4( 293 Votes )

# The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4cm. Find the radius of the circle.

Answer :

Let us consider a circle centred at point O.

AB is a tangent drawn on this circle from point A.

Given that,

OA = 5cm and AB = 4 cm

In ΔABO,

OB ⊥ AB (Radius ⊥ tangent at the point of contact)

Applying Pythagoras theorem in ΔABO, we obtain

AB^{2} + BO^{2} = OA^{2}

4^{2} + BO^{2} = 5^{2}

16 + BO^{2} = 25 BO^{2} = 9

BO = 3

Hence, the radius of the circle is 3 cm.

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