A circle with 20 cm radius is dividedinto four equal parts by three concentric circles Find out the radii - Maths -

Question

A circle with 20 cm radius is dividedinto four equal parts by three
concentric circles Find out the radii of those three concentric
circles

Devesh Kumar · Accepted Answer

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
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"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_556ea9a4977e2%20png"
style="width: 1018px; height: 564px; float: left;">
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

A circle with 20 cm radius is dividedinto four equal parts by three concentric circles. Find out the radii of those three concentric circles.