Question

A chord of length 8 cm is drawn at a distance of 3 cm from the centre of a circle. Calculate the radius of the circle.

Answer 1

Let $AB$ be the chord and $O$ be the centre of the circle
Let $OC$ be the perpendicular drawn from $O$ to $AB$
We know, that the perpendicular to a chord, from the centre of a circle, bisects the chord.
$\therefore AB=8cm$
$A{C}^2=C{B}^2=\frac{AB}{2}$
$A{C}^2=C{B}^2=\frac{8}{2}$
$A{C}^2=C{B}^2=4cm$
In $△OCA$,
$O{A}^2=O{C}^2+A{C}^2$ (BY Pythagoras theorem)
$\Rightarrow O{A}^2=(3{)}^2+(4{)}^2=9+16=25$
$\Rightarrow OA=5cm$
Hence, radius of the circle is $5cm$.