In each of the following, write true or false and justify your answer. Tangent length from an external point on a circle is always greater than circle radius. 

To get the required result, first draw a circle with two tangents touching it with the same external point, then join the points touching the circle and the centre, and finally join the centre of the circle to the external point.

Consider any point P that is outside of a circle and away from 0.

Draw tangent PA on the circle now. Clearly.

$PA>r$[Because $P$is outside the circle,  $P$is a sufficient distance away]

 Now, consider any point $P_1$on the tangent AP that is very close to contact point A of the tangent $PA,P_{1}A<AO$

As a result, the lengths of the tangents $PA$ and $P_{1}A$are greater and smaller than the radius OA, respectively.

As a result, the length of a tangent from an external point of a circle can be greater or less than the radius of the circle. 

As a result, the given statement is false.