Question

In the diagram two equal circles of radius 4 em 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

Answer 1

The correct option is B $4\sqrt{3}cm$

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