Write 'True' or 'False' and give reasons for your answer.
The length of the tangent from an external point $P$ on a circle with centre $O$ is always less than $OP$.
The length of the tangent from an external point $P$ on a circle with centre $O$ is always less than $OP$.
(TRUE) True.
Let $PT$ be the tangent drawn from an external point $P$ to the circle at point of contact $T$. Join $OT$.
Since the radius is perpendicular to the tangent at the point of contact,we have $OT \perp PT$.
Thus,$\triangle OPT$ is a right-angled triangle with $\angle OTP = 90^{\circ}$.
In a right-angled triangle,the hypotenuse is the longest side. Here,$OP$ is the hypotenuse.
Therefore,$OP > PT$,which implies that the length of the tangent $PT$ is always less than $OP$.
Let $PT$ be the tangent drawn from an external point $P$ to the circle at point of contact $T$. Join $OT$.
Since the radius is perpendicular to the tangent at the point of contact,we have $OT \perp PT$.
Thus,$\triangle OPT$ is a right-angled triangle with $\angle OTP = 90^{\circ}$.
In a right-angled triangle,the hypotenuse is the longest side. Here,$OP$ is the hypotenuse.
Therefore,$OP > PT$,which implies that the length of the tangent $PT$ is always less than $OP$.
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