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

Solution :

Given: 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 ⊥ AC Proof:

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 ⊥ AC || The shortest line sgement drawn from a given point to a given line , is ⊥ to the line. Proved