Two concentric circles are shown. If the area of the shaded region is equal to the area of the non-shaded region. what is the ratio of the radius of the larger circle to the radius of the smaler circle? Express your answer in simplest radical form.

mathleteig Feb 2, 2020

#1**+2 **

small circle area = pi r^2 is equal to Large circle area (pi L^2) minus small circle area(pi r^2)

pi r^2 = pi L^2 - pi r^2

2 pi r^{2} = pi L^{2}

2 r^{2 }= L^{2}

2 = L^{2} / r^{2}

sqrt2 = L / r

ElectricPavlov Feb 2, 2020