Apr 15, 2015

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

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


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