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

Solution:

Let P be a point external to the circle away from O

Construct a tangent PA on the circle

PA > r

Now, let us consider a point P1 on the tangent AP near to contact point A of tangent

PA, P₁A < AO

The length of tangent PA and P₁A are greater and smaller than the radius OA

So the length of tangent may or may not be greater than the radius

Therefore, the statement is false.

✦ Try This: Prove that the lengths of tangents drawn from an external point to a circle are equal.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10

NCERT Exemplar Class 10 Maths Exercise 9.2 Problem 2

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

Summary:

The statement “The length of tangent from an external point on a circle is always greater than the radius of the circle” is false

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