Question

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

Answer 1

(i) False
Because the length of tangents from an external point P on a circle may or may not be greater than the radius of the circle.
(1 mark)
(ii) True
PT is a tangents drawn from external point P . Join OT
$\therefore OT\perp PT$
So, OPT is a right angled triangle formed
In right angled triangle, hypotenuse is always greater than any of the two sides of the triangle.
$\therefore$ OP > PT
Or PT < OP (1 mark)