Question

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

Answer 1

$O^{\prime }$ is centre and from the figure given below,

Let $O^{\prime }$ be center of circle
perpendicular distance from center $O^{\prime }$ from $y=0$ i.e., $x-$axis
$d=4$
Now from diagram,
$6=2\sqrt{r^2-16}\Rightarrow r=5$ units