Question

Question 6
The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

Answer 1

AB is a tangent drawn on this circle from point A.
$\therefore OB\perp AB$
OA = 5cm and AB = 4 cm (Given)
In $\Delta$ ABO,
By Pythagoras theorem in $\Delta$ ABO,
$O{A}^2=A{B}^2+B{O}^2$
$\Rightarrow 5^2=4^2+B{O}^2$
$\Rightarrow B{O}^2=25-16$
$\Rightarrow B{O}^2=9$
$\Rightarrow BO=3$
$\therefore$ The radius of the circle is 3 cm.