What is the value of  $AC$if radius of circle is 5cm and  $OB= 3cm$?

 

Concept: A chord is a line segment that connects any two points on a circle's circumference. The perpendicular from the centre of a circle bisects the chord.

Here, radius of circle  =5 cm

So, $OA=OC=5 cm$

In  $∆BOC,\angle OBC={90}^0$ and $OB=3 cm$

By Pythagoras theorem, 

$O{C}^2=O{B}^2+B{C}^2$

$\Rightarrow 5^2=3^2+B{C}^2$

$\Rightarrow 5^2-3^2=B{C}^2$

$\Rightarrow B{C}^2=25-9=16$

$\Rightarrow BC=4 cm$

Since perpendicular from centre to a chord bisects the chord, $AB=BC$

$\Rightarrow AC=2BC=8 cm$

Hence, the value of  AC is  $8 cm$.