Contents
In this publication, we will consider formulas with which you can calculate the radius of a circle circumscribed about a square. We will also analyze examples of solving problems to consolidate the material presented.
Formulas for calculating the radius of the circumscribed circle
Through the side of the square
Radius R the circumscribed circle of a square is equal to the length of its side atimes the square root of two and divided by two.
Through the diagonal of the square
Radius R circumscribed around the square of a circle is equal to half of its diagonal d.
Examples of tasks
Task 1
The length of the side of the square is 8 cm. Find the radius of the circle circumscribed around it.
Solution
Let’s apply the first formula discussed above:
Task 2
Calculate the length of the diagonal of a square if the radius of the circumscribed circle is 6 cm.
Solution
As we know, the radius of the circumscribed circle is equal to half the diagonal of the square. Therefore, the total length of the diagonal is 12 cm (6 cm ⋅ 2).