2.152636 cm. = (12 x 8) – (16 x pi ) this is the area of the small circle ( 45.734 squared cms ) the squared root of this amount is divided by pi ( 3.14159 ) it give you 2.152636 cm.

nevermind that was dumb but how do you account for the area of the rest of the rectangle?

Another method that give me 2.157 cms is to draw a circle half the size of the big circle (2 cms) and place it at the center of the small circle by making an octagono I get that the circumscribe lenght of 2.157 cms.

is there a piece of information missing? As I have tried several strategies and keep getting r = r or 4 = 4

Are you using the 12? And pythagoras…

sorry ignore my comment I think I’ve solved it !

2.14359?

I get 2.1444 cms

Sorry is r2 = 2.14359360665022975737527008 cms

Yes

I’m not seeing it

Draw a right angled triangle where the hypotenuse is the 2 radii as shown

i got 1

Is it 2cm?

Yes and no, if you consider that (4- X)+(8-X)=4+X

2.152636 cm. = (12 x 8) – (16 x pi ) this is the area of the small circle ( 45.734 squared cms ) the squared root of this amount is divided by pi ( 3.14159 ) it give you 2.152636 cm.

height of the rectangle is not 8…

nevermind that was dumb but how do you account for the area of the rest of the rectangle?

Another method that give me 2.157 cms is to draw a circle half the size of the big circle (2 cms) and place it at the center of the small circle by making an octagono I get that the circumscribe lenght of 2.157 cms.

Final answer is a quadratic equation in r2 = (4 – r2) squared + ( 8 – r2 ) squared = ( 4 + r2 ) squared.

So I get 2.1444 cms