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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 the tangent from an external point P on a circle with center O is always less than OP.

Answers (1)

Answer True
Solution
             
 

Here O is the center of the given circle and PA is the tangent which is drawn from an external point P. OA is the radius of the circle. We know that tangent and radius are always perpendicular to each other.
\therefore \, \angle A= 90^{\circ}
 \therefore \bigtriangleup PAO is a right-angle triangle Use Pythagoras's 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 the hypotenuse is always greater than the length of the perpendicular in a right-angle triangle.
i.e.,      OP > PA
Hence the given statement is True.


   

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