question_answer

In the diagram two equal circles of radius 4 cm intersect each other such that each passes through the centre of the other. Find the length of the common chord.  

A) \[2\sqrt{3}\,cm\]

B) \[4\sqrt{3}\,cm\]

C) \[4\sqrt{2}\,cm\]

D) \[8 cm\]          

Correct Answer: B

Solution :

 If O and O' be the centres, then OO' will be the common radius. \[\therefore \]  \[OO'=4\,cm\] \[\therefore \]  \[OA=PB=O'A\]                 \[=O'B\] (because these are radii) \[\therefore \]  \[OAO'B\] is a rhombus. But the diagonals of a rhombus intersect each other at right angle.                 \[\therefore \]  \[\angle AEO={{90}^{o}}\] \[\therefore \]  \[A{{E}^{2}}+O{{E}^{2}}=A{{O}^{2}}\] or            \[A{{E}^{2}}+4=16\]                 \[AE=\sqrt{12}\]                 \[=2\sqrt{3}\] \[\therefore \]  \[AB=2\times 2\sqrt{3}\]                 \[=4\sqrt{3}\]