What is the radius of the circle in terms of the edge length of the square?

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- May 8th 2006, 01:08 PMNatasha1A semi-circle in a square.
What is the radius of the circle in terms of the edge length of the square?

- May 8th 2006, 01:57 PMCaptainBlackQuote:

Originally Posted by**Natasha1**

as shown in the diagram (a point from which the diameter of a circle

subtends a right angle is on the circle).

We can see from the diagram that the diagonal of the square is:

$\displaystyle

r+\sqrt{2 r^2}

$,

now if the side of the square is $\displaystyle s$ the diagonal is:

$\displaystyle

\sqrt{2 s^2}=r+\sqrt{2 r^2}

$,

from which you can finish the problem.

RonL - May 28th 2006, 08:20 AMSoroban
Lovely solution, Captain Black!

- May 28th 2006, 09:04 AMCaptainBlackQuote:

Originally Posted by**Soroban**

RonL