In this question we aim to prove that the tangent is perpendicular to the radius drawn from its point of contact.
In the diagram, $C$C is an arbitrary point on the line $AD$AD, and $B$B is the point at which the tangent meets the circle.
What can we say about the lines $OB$OB and $OC$OC?
What point on $AD$AD is closest to the centre of the circle?
In general, what can we say about the angle of a line joining some point to some other line by the shortest route?
Hence, what can we say about angle $\angle OBA$∠OBA?