In the given figure. PQ = 30. RS = 24 and OM = 12. then what is the value of ON? 

Given :  PQ = 30, RS = 24 and OM = 12

To find : ON = ?

Solution : A perpendicular from the centre of a circle to the chord bisects it.

=> MQ = $$\frac{3}{2}=15$$ and NS = 12

In $$\triangle$$ OMQ,

=> $$(OQ)^2=(OM)^2+(MQ)^2$$

=> $$(OQ)^2=(12)^2+(15)^2$$

=> $$(OQ)^2=144+225=369$$

Also, OQ = OS = radii of circle

Similarly, in $$\triangle$$ ONS,

=> $$(ON)^2=(OS)^2-(NS)^2$$

=> $$(ON)^2=369-(12)^2$$

=> $$(ON)^2=369-144=225$$

=> $$ON=\sqrt{225}=15$$

=> Ans - (C)