A circle with 20 cm radius is dividedinto four equal parts by three concentric circles. Find out the radii of those three concentric circles. Share with your friends Share 1 Devesh Kumar answered this Below is a diagram representing the 4 concentric circles 1,2,3,4 with regions A,B,C,DRegion A=circle1Region B=circle2-circle1Region C=circle3-circle2Region D=circle4-circle3Let radius of circle1=r1 radius of circle2=r2 radius of circle3=r3 radius of circle4=r4=20cm given Now, Area of regionA= Area of regionB= Area of regionC= Area of regionBπr12=πr22-r12=πr32-r22=πr42-r32r12=r22-r12=r32-r22=202-r32here we have 3= signs i.e 3eqs, we should move from L.H.S as there are r2 can be expressed as r1& further r3 also. finally we reach to r4 which is known.From 1st eq⇒r22=2r12 From 2nd eq⇒r32=2r22-r12=2×2r12-r12=3r12From 3rd eq⇒r42=2r32-r22=2×3r12-2r12=4r12⇒r42=202=4r12⇒ r1=10cm Taking only the positive sign⇒r22=2r12=2×102⇒r2=102=14.14cm⇒r32=3×102⇒r3=103=17.32cmAnswer r1=10cm,r2=14.14cm,r3=17.32cm 0 View Full Answer