a circle with area A1 is contained in the interior of a larger circle with area A1 +A2. if the radius of the larger circle is 3units and A1,A2,A1+A2 are in A.P. , then the radius of the smaller circle is ---?

Ok

Let The Area Of Larger Circle Be A3 Thus A1+A2

Its Given That Radius Of Larger Circle Is 3 Units

So Apply Formula Of Area Of Circle

We Get

Pie*3*3 = 9*Pie

Now Its Given That Areas Are In AP 

So There Is A Common Difference Between Them

A2-A1 = A3-A2

2A2-A1 = A3

Now Value Of A3 Is Known 

Also A2+A1 = A3

Now Replacing Values We Get

A2+A1 = 2A2-A1

2A1 = A2

Hence We Get That Every Area Is Double Of Other

So A3 = 2A2

And A3 = 4A1

Now 

A3 = 9*Pie

9*Pie = 4A1

A1 = 9*Pie/4

Let The Radius Of Smaller Circle Be r

Pie*r*r = 9*Pie/4

r² = 9*Pie/4*Pie = 9/4

r = 3/2

So Radius Of Smaller Circle Is 3/2 Units