Question

The area of a circle is A and that of a larger circle is A + B. If A, B, and A+B are in AP and the radius of the larger circle is 3, find the radius of the smaller circle

Answer 1

@Mimi_x3

Answer 2

@ganeshie8

Answer 3

Could you draw it?

Answer 4

there is no diagram provided

Answer 5

I mean, with your question

Answer 6

i dont think you need one cos you can just use the given info

Answer 7

K

Answer 8

@Compassionate @Hero @ikram002p

Answer 9

Let's do this!

Answer 10

Yay!

Answer 11

First of all, it is given that \(A + B = \pi \times \underbrace{3^2}_{\rm radius^2} = 9\pi.\)

Secondly, the condition \(x,y,z\) to be in AP is \(2y = x + z\). Let's use that.

Here, \(A, B, A + B\) is the AP. Therefore \(2B = A + A + B \Rightarrow B = 2A\).

Now, we have two equations. Let's solve them.\[A + B = 9\pi\]\[\iff A + 2A = 9\pi\]\[
\iff 3A = 9\pi\]\[\iff A = 3\pi\]And so, the radius of the smaller circle would be \(3\pi\) sq. units.

Answer 12

The area of the smaller circle*

Answer 13

The radius should be easy to find, though, because you know the area.

Answer 14

thanks

Answer 15

\[Area=\pi*r^2\]\[3\pi=\pi*r^2\]\[\frac{3\pi}{\pi}=r^2\]\[\frac{3\cancel{\pi}}{\cancel\pi}=r^2\]\[3=r^2\]\[r=\pm\sqrt{3}\]

Answer 16

Not \(\pm \sqrt 3\) - just \(\sqrt 3\) :)