Two circles, each of unit radius, are so drawn that the center of each lies on the circumference of the other. Find the area of the region which is common to both the circles

Answers (1)


Consider the traingle AOB,
ob=0.5 units
ab=1 unit
Rightarrow OA=sqrt1^2-0.5^2=fracsqrt32, units
Total area of the traingles AOB and BOC=fracsqrt34
Area of intersection=2(Area of sector-Area of traingles)
Area of sector ab=frac12r^2angle abc=fracpi3
Rightarrow 2(fracpi3-fracsqrt34)
Rightarrow frac4pi-3sqrt36, sq., units
 

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