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  • Write ‘True’ or ‘False’ and justify your answer in each of the following : The length of tangent from an external point P on a circle with centre O is always less than OP.

Write ‘True’ or ‘False’ and justify your answer in each of the following :The length of tangent from an external point P on a circle with centre O is always less than OP.

Answers (1)

Answer True
Solution
             
 

Here O is the center of given circle and PA is tangent which is drawn from an external point P. OA is radius of circle.We know that tangent and radius is always perpendicular to each other.
\therefore \, \angle A= 90^{\circ}
 \therefore \bigtriangleup PAO is a right angle triangle Use Pythagoras theorem in \bigtriangleup PAO
       \left ( PO \right )^{2}= \left ( OA \right )^{2}+\left ( PA \right )^{2} …..(i)
From equation (i) we can say that PA is always less than PO.
  In other words we can say that the length of hypotenuse is always greater than the length of perpendicular in a right angle triangle.
i.e.,      OP > PA
     Hence the given statement is True.


   

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