Question

From an external point $Q$, the length of tangent to a circle is $12cm$ and the diatance of $Q$ from the centre of circle is $13cm$. The radius of circle (in $cm$ ) is

• A. 10
• B. 7
• C. 5
• D. 12

Answer 1

The correct option is C 5

Let $O$ be the centre of the circle. As per given information we have drawn the fig as below.
We have $OQ=13cm$
and $PQ=12cm$
Radius is perpendioular to the tangent at the point of contaot
Thus $OP\perp PQ$
In $△OPQ$, using Pythagoras theorem,
$$\begin{array}{cc}O{I}^2+P{Q}^2& =O{Q}^2\\ O{P}^2+{12}^2& ={13}^2\\ U{P}^2& ={13}^2-{12}^2\\ & =169-144\\ & =25\end{array}$$
Thus $OP=5cm$