Circles within circles question ...

[pazzy78]

Not looking for the solution, I am currently working on it but someone else mentioned that the radius of the outer circle is the sum of the 2 radii of the inner circles, i don't know if this is a rule ... or he is assuming it's part of the problem ..

is it a rule ?

 

[pazzy78]

omg ... i apologise for the silly q...

if radius of inner circles are a and b ...
diameter of outer circle = 2a + 2b

radius = a + b.

dohhh...

 

[fresh_42]

Hint: use the chord formula [imath] \overline{PQ} =2\sqrt{r^2-(r-h)^2}= 2\sqrt{2rh-h^2}[/imath] where [imath] r=a+b [/imath] and [imath] h=2a [/imath] in case [imath] a\leq b. [/imath] The area calculation will eliminate [imath] b. [/imath]

... and post your result. I want to know whether I made a mistake in my scribblings ;-)