Given in the question,

OT = radius = $8cm$

OP = $17cm$

It is given to find: PT = length of tangent =$?$

T is point of contact. We also know that the tangent and radius are perpendicular at the point of contact..

∴ OTP is right angled triangle $\angle OTP={{90}^{\circ }}$ , and according to Pythagoras theorem the square of hypotenuse is equals to the sum of square on the other two sides.

So,

$O{{P}^{2}}=O{{T}^{2}}+P{{T}^{2}}$

${{17}^{2}}={{8}^{2}}+P{{T}^{2}}$

$P{{T}^{2}}={{17}^{2}}-{{8}^{2}}$

$PT=\sqrt{289-64}$

$PT=\sqrt{225}$

$PT=15cm$ is the length of Tangent.