OpenStudy (anonymous):

The side length of the square is 8cm. I need help figuring out the radius of the inscribed and the circumscribed circles. Please help! I may not respond immediately, I may have to run soon.

OpenStudy (mathstudent55):

|dw:1459782475291:dw|

OpenStudy (mathstudent55):

The inscribed circle is simple.

OpenStudy (anonymous):

Alright. So its 4cm, really?

OpenStudy (mathstudent55):

Right.

OpenStudy (mathstudent55):

Now we need to look at the circumscribed circle.

OpenStudy (mathstudent55):

|dw:1459782643530:dw|

OpenStudy (mathstudent55):

Use the Pythagorean theorem to find x, the radius of the circumscribed circle. |dw:1459782878745:dw|

OpenStudy (anonymous):

Ok, I will. ALso, sorry for disapearing.

OpenStudy (anonymous):

Is it 128?

OpenStudy (mathstudent55):

$$a^2 + b^2 = c^2$$ $$c^2 = a^2 + b^2$$ $$x^2 = (4~cm)^2 + (4~cm)^2$$ $$x^2 = 16~cm^2 + 16~cm^2$$ $$x^2 = 32~cm^2$$ $$x = \sqrt{32~cm^2}$$ $$x = \sqrt{16 \times 2~cm^2}$$ $$x = 4\sqrt 2~cm$$