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
Solution:
Let us consider the figure
PT is the tangent from the external point P
Join OT
OT ⏊ PT
We know that
A tangent at any point on the circle is perpendicular to the radius through the point of contact.
OPT is a right-angled triangle formed.
In a right angled triangle, the hypotenuse is always greater than any of the two sides of the triangle.
OP > PT or PT < OP
The length of tangent from an external point on a circle is always less than the radius of the circle.
Therefore, the statement is true.
✦ Try This: The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10
NCERT Exemplar Class 10 Maths Exercise 9.2 Problem 3
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
Summary:
The statement “The length of tangent from an external point P on a circle with centre O is always less than OP” is true
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