# circle problem

• Oct 30th 2008, 07:42 AM
david18
circle problem
Attachment 8465

I'm having trouble with this question. For the first part Im guessing that the radius is 2 times larger for the bigger circle and therefore its area is four times as large, but I can't seem to prove that the radius is twice as large.

I'd appreciate it if anyone could help me out on this question
• Oct 30th 2008, 09:04 AM
vincisonfire
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?
• Oct 30th 2008, 02:03 PM
david18
thanks for the help.

I'm also a bit stuck on the second part, any ideas on what to do?
• Oct 30th 2008, 02:08 PM
vincisonfire
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 $\displaystyle \frac{2 \cdot(3\cdot\sqrt(3)-2\cdot \pi)}{\pi-6\cdot\sqrt(3)}$
• Nov 9th 2008, 11:32 AM
bjhopper
circle problem
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