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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 $3 \mathrm{~cm}$.
Updated on: 10-Oct-2022
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