+110 Three concentric circles are drawn such that the area of the smallest circle is equal to the area of each of the rings. If the radius of the largest circle is 12 cm, what is the radius of the smallest circle?
+128407 Call S the radius of the smallest circle and M the radius of the intermediate circle
pi (12)^2 - pi (M)^2 = pi ( S)^2 (1) and
pi (M)^2 - pi(S)^2 = pi (S)^2 ⇒ pi (M)^2 = 2 pi (S)^2 (2)
Sub (2) into (1)
pi (12)^2 - 2pi(S)^2 = pi (S)^2
12^2 - 2S^2 + S^2
12^2 = 3S^2
144 = 3S^2
48 = S^2
√48 = S
4√3 cm = S ≈ 6.93 cm
