(c) Let the radius of the semicircle be R.Now join O to B OC = OD = R ∴OB=R√2 The diameter of the smaller circle=(R√2−R)=R(√2−1) Area of the semicircle =
πR2
2
; Area of the circle =
πR2(√2−1)2
22
Hence the ratio of the area of the smaller circle to that of the semicircle =