# A semi-circle in a square.

• May 8th 2006, 02:08 PM
Natasha1
A semi-circle in a square.
What is the radius of the circle in terms of the edge length of the square?
• May 8th 2006, 02:57 PM
CaptainBlack
Quote:

Originally Posted by Natasha1
What is the radius of the circle in terms of the edge length of the square?

Draw in the rest of the circle, it will pass through the corner of the square
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:

$
r+\sqrt{2 r^2}
$
,

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

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

from which you can finish the problem.

RonL
• May 28th 2006, 09:20 AM
Soroban
Lovely solution, Captain Black!
• May 28th 2006, 10:04 AM
CaptainBlack
Quote:

Originally Posted by Soroban
Lovely solution, Captain Black!

Thank you.

RonL