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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 on a circle is always greater than the radius of the circle.

Write ‘True’ or ‘False’ and justify your answer in each of the following: The length of the tangent from an external point on a circle is always greater than the radius of the circle.

Answers (1)

Answer False
Solution
Case-I – When external point P is very close to the circle
      
Here C is the center of the circle. Let this radius be 5 and the distance of Px and Py is 3. Or we can say that Case I contradicts the given statement.
Case II – When external point P is far from the circle.
 
Here radius of the given circle is 5 cm and the length of Px and Py is 10 cm.
Hence according to Case II and given statement is True.
Hence from the above two cases, we conclude that the tangent’s length is dependent on the distance of an external point from the circle.
Therefore given statement is False because the length of the tangent from an external point of a circle may or may not be greater than the radius of the circle.
Therefore the given statement is False.

 

 

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