Question 1156648
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The tangent line (the tangent segment) is perpendicular to the radius, drawn to the tangent point.


So, you have rigth angle triangle with the hypotenuse 15+2 = 17 units and one leg of 15 units (the radius).


Then the other leg (which is the tangent segment) is


    {{{sqrt(17^2 - 15^2)}}} = {{{sqrt(289-225)}}} = {{{sqrt(64)}}} = 8 units.


<U>ANSWER</U>.  The tangent segment PC is 8 units long.
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Solved.