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


OB AB (Radius tangent at the point of contact)

Applying Pythagoras theorem in ΔABO, we obtain

AB2 + BO2 = OA2

42 + BO2 = 52

16 + BO2 = 25 BO2 = 9

BO = 3

Hence, the radius of the circle is 3 cm.

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