Question Number 103872 by mikolo last updated on 17/Jul/20

Commented bybramlex last updated on 18/Jul/20

Commented bybramlex last updated on 18/Jul/20

AB^2  = AD^2  + BD^2   (2+r)^2  = 4 + (4−r)^2   (2+r)^2 −(4−r)^2  = 4  (6)(2r−2) = 4 ⇒ r−1 = (1/3)  ∴ r = (4/3) .

Commented bybramlex last updated on 18/Jul/20

the shaded area A= (1/2)π(4)^2 −π(2)^2 −π((4/3))^2   A= 8π−4π−((16π)/9) = ((20π)/9).