Two circles of radius r fit inside a square of side length s. Find r in terms of s, and then find the area of the shaded region in terms of s.

Guest Feb 16, 2021

#1**0 **

Connect the centers of the circles. You will get a line of length 2r.

You can also draw a line starting at the center higher circle going downward and a line starting at the center of the lower circle to form an isosceles right triangle with hypotenuse 2r.

The side length of a leg of the isosceles right triangle is \(r\sqrt{2}\).

Therefore, the side length (s) = \(2r + r\sqrt2\).

Guest Feb 16, 2021