A point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.
Given:
A point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 10 cm.
To do:
We have to find the radius of the circle.
Solution:
$TP = 10\ cm$ and $OP = 26\ cm$
$PT$ is the tangent to the circle at $T$.
$OT\ perp\ PT$
In right angled triangle $OTP$,
By Pythagoras theorem,
$OP^2= OT^2+ TP^2$
$26^2 = OT^2 + 10^2$
$OT^2= 676 - 100$
$= 576$
$= 24^2$
Therefore,
$OT = 24\ cm$
The length of the radius of the circle is 24 cm.
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