Question

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

Answer 1

Given : A circle touches the $y-$axis at $(0,4)$ and cuts the

$x-$axis at the points $A$ and $B$.Let $P$ be the centre of the circle.

$\therefore PM=4$units

And the perpendicular $PM$ bisects the chord $AB$

$\therefore AM=MB=3$units since $AB=6$units

From $△PAM,{AP}^2={AM}^2+{PM}^2$

$\therefore {AP}^2=3^2+4^2=9+16=25$

$\therefore$ Radius of the circle$=AP=5$units.