A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :

Suppose we have a figure as shown, the line that is drawn from the centre of the given circle to the tangent PQ is perpendicular to PQ. 

Now since OP ⊥ PQ, we have ΔOPQ as a right-angle triangle,

Using Pythagoras’ theorem,

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

${\left(12\right)}^2 = 5^2+P{Q}^2$

$P{Q}^2 = 144-25$

$P{Q}^2 = 119$

$PQ = \sqrt{119}cm$

Thus, option D is the correct answer.