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

Answer :

Since tangent to a circle is perpendicular to the radius through the point of contact,

$$\therefore$$ $$∠ \ OTA \ = \ 90°$$

In $$∆ \ OTA$$, we have

$$\Rightarrow OA^2 \ = \ OT^2 \ + \ AT^2 \$$
$$\Rightarrow \ 5^2 \ = \ OT^2 \ + \ 4^2$$
$$\Rightarrow \ OT^2 \ = \ 5^2 \ - \ 4^2 \ = \ 25 \ - \ 16 \ = \ 9$$

$$OT \ = \ \sqrt{9} \ = \ 3$$

$$\therefore$$ Radius of the circle is 3 cm.