Question

A circle touches the $y$-axis at the point $(0,4)$and cuts the $x$-axis in a chord of length $6$ units. The radius of the circle is

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is C

$5$

The explanation for the correct option:

Step1. Draw the diagram :

Step-2. Calculate the radius :

In the triangle, $AO\text{'}C$ we have

$O\text{'}C=4,andOA=r\left(let\right)$

Since $O\text{'}C$ is perpendicular on $AB$. So, it divide $AB$into two equal parts then

$AC=3$

By Using Pythagoras' theorem In the triangle, $AO\text{'}C$. we have

$$\begin{gathered} \Rightarrow O\text{'}{A}^2=O\text{'}{C}^2+A{C}^2 \\ \Rightarrow r^2=4^2+3^2 \\ \Rightarrow r=\sqrt{16+9} \\ \Rightarrow r=5 \end{gathered}$$

Hence, the correct option is C.