Theorem :Tangent and radius of a circle are perpendicular to each other.

Solution :

A circle with centre O.
AB is the tangent to the circle at point B
and OB is the radius of the circle.
R.T.P. OB &#x22A5 AC

1.  OB < OC || Since each point of the tangent other than point B is outside the circle. 2.  Similarly it can be shown that out of all the line segments which would be drawn from point O to the tangent line AC, OB is the shortest. 3.   OB &#x22A5 AC || The shortest line sgement drawn from a given point to a given line , is &#x22A5 to the line.

READ :  Theorem | the angle subtended by an arc of a circle | at the centre is double the angle subtended by it at | any point on the remaining part of the circle