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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.

Given:

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

To do:

We have to find the radius of the circle.

Solution:

Let OP be the radius of a circle.

$OAP$ is a right angled triangle.

Therefore,

$OA^2=AP^2+OP^2$

$5^{2}=4^{2}+\mathrm{OP}^{2}$25=16+\mathrm{OP}^{2}$

$\mathrm{OP}^{2}=25-16$

$\mathrm{OP}^{2}=9$ $\mathrm{OP}=\sqrt{9}$

$\mathrm{OP}=3 \mathrm{~cm}$

The radius of the circle is $3 \mathrm{~cm}$.

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