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, |
\[OA=\sqrt{O{{C}^{2}}+C{{A}^{2}}}=\sqrt{{{6}^{2}}+{{8}^{2}}}\] |
\[=\sqrt{36+64}=\sqrt{100}=10\,\,cm\] |
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