Theorem: Tangent and Radius of a Circle | are Perpendicular to Each Other.

mc8sz_theorem

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 &#x22A5 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 &#x22A5 AC || The shortest line sgement drawn from a given point to a given line , is &#x22A5 to the line.
Proved

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