Thread: A semi-circle in a square.

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

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:

,

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

,

from which you can finish the problem.

RonL

Lovely solution, Captain Black!

Originally Posted by Soroban

Lovely solution, Captain Black!

Thank you.

RonL