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Find the length of a tangent drawn to a circle with radius 5 cm, from a point 13 cm from the centre of the circle.
Given:
Radius of the circle $=5\ cm$.A point is 13 cm from the centre of the circle.
To do:
We have to find the length of the tangent.
Solution:
Let $O$ be the centre of the circle, $P$ be the point 13 cm from the centre of the circle and $PT$ be the tangent to the circle meeting it at $T$.
$OT = 5\ cm$ and $OP = 13\ cm$
$PT$ is the tangent to the circle at $T$.
$OT\ perp\ PT$
In right angled triangle $OTP$,
By Pythagoras theorem,
$OP^2= OT^2+ TP^2$
$13^2 = 5^2 + TP^2$
$TP^2= 169 - 25$
$= 144$
$= 12^2$
Therefore,
$TP = 12\ cm$
The length of the tangent is 12 cm.
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