If c is the length of side of triangle
Height is $\displaystyle \sqrt{\frac{3}{2}} c $ by pythagore theorem
Height is $\displaystyle r_{small} + r_{large} $
Draw a rectangle triangle which hypothenuse is $\displaystyle r_{large} $ and one of small side $\displaystyle r_{small} $
You find that $\displaystyle r_{large} = \frac{\sqrt{3} \cdot c}{3}$
$\displaystyle r_{small} = \frac{\sqrt{3} \cdot c}{6}$
And you were right.
Ok for the rest?
Of course, the first question is $\displaystyle \frac{4}{1} $ because
$\displaystyle A = \pi r^2 $ if r is twice as large than area is four time bigger.
$\displaystyle area_{curve triangle} = \frac{area_{triangle} - area_{small circle}}{3} $
$\displaystyle area_{arc of circle} = \frac{area_{large circle } - area_{triangle}}{3} $
You know all you need to calculate these area with what I told you
Answer is $\displaystyle \frac{2 \cdot(3\cdot\sqrt(3)-2\cdot \pi)}{\pi-6\cdot\sqrt(3)} $
posted by david 18 and answered by vincesonfire
this problem is simplified by taking unity as the radius of the large circle.Following vinci formulars iget an answer as follows
3/4xradical 3-pi/4 dividedby pi-3/4 xradical 3 and numerically slightly lower than the previous answer and does not generate negative numbers
bj