Two circles having radii r units intersect each other in

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Two circles having radii r units intersect each other in such a way that each of them passes through the centre of the other. Then the length of their common chord is

According to question , we draw a figure of two circles with centres C and D ,

CO = OD =	r	units
	2

AC = r units
In ∆ AOC,
OA = √AC² - OC²

= √	r² -	r²	= √	3r²	=	√3r
		4		4		2

∴ AB = 2OA = 2 ×	√3r
	2

AB = √3r units