MCQ Solution: Circles

If two equal circles of radius r passes through centre of the other then the length of their common chord is

1) r / Ö3
2) r Ö3
3) Ö3 r / 4
4) r Ö2

SOLUTIONS 

We know that, if two circles intersect each other, the line joining the centres in perpendicular bisector of  common chord.

In D AOO'

Since all the sides are equal to ' r', therefore DAOO' is an equilateral triangle.

 all angles are 60° 

sin 60° =  AM / AO

Ö3 /2  =  AM /  r 

 AM  = Ö3 r/2  

AB = 2AM  = Ö3 r/2  x 2  

= r Ö

 

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