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.


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


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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