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