question_answer

If two equal circles, whose centres are O and  O', intersect each other at the points A and B,

OO' = 12 cm and AB = 16 cm, then the radius of the circles is                                                      [SSC (CGL) 2012]

A) 10 cm

B) 8 cm 

C) 12 cm              

D) 14 cm

Correct Answer: A

Solution :

Given,   \[AB=16\,\,cm\]

\[\therefore \]      \[AC=BC=8\,\,cm\]

and       \[OO'=12\,\,cm\]

\[\therefore \]      \[OC=CO'=6\,\,cm\]

In \[\Delta OAC,\]by Pythagoras theorem,

\[OA=\sqrt{O{{C}^{2}}+C{{A}^{2}}}=\sqrt{{{6}^{2}}+{{8}^{2}}}\]

\[=\sqrt{36+64}=\sqrt{100}=10\,\,cm\]