Find the length of tangent to a circle from a point at a distance of 5 cm from center of the circle of radius 3 cm.

Given:

Radius of the circle$=3\ cm$.

Distance of the point from the centre of the circle$=5\ cm$.

To do:

We have to find the length of the tangent.

Solution:

Let O be the centre of the circle.

Radius $OP=3\ cm$.

$OT=5\ cm$

TP is a tangent. This implies,

$\angle OPT=90^o$

In right-angled triangle OPT,

$OT^2=TP^2+OP^2$

$5^2=TP^2+3^2$

$TP^2=25-9$

$TP^2=16$

$TP=\sqrt{16}$

$TP=4\ cm$

The length of the tangent is $4\ cm$. 

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Updated on: 10-Oct-2022

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