Let us suppose that there is a circle having radius OP.

Let there is a tangent AB Which touches the circle.

Now Take a point Q on line AB and join with O. 

Here OQ is greater than OP. 

Now every point on the line AB like Q₁ , Q₂ , Q₃ ,...

OQ₁ > OP

OQ₂ > OP

OQ₃ > OP

and so on.

So OP is the shortest distance Between the point P and line Segment AB.

Hence OP is perpendicular to AB.