Since angle A = angle C, by sine rule, b/sin2C=(b-r/4)/sinC, i.e. b/(b-r/4)=2cosC. Let D be the centre. tan angleDCA = r/(b/2), i.e. tanC/2 = 2r/b Since cos C = (1-t^2)/(1+t^2) where t=tanC/2, b/(b-r/4) = 2[(1-4r^2/b^2)/(1+4r^2/b^2)] b(b^2+4r^2)=2(b-r/4)(b^2+4r^2) b^3-rb^2/2+4r^2b-2r^3=0 (b-r/2)(b^2+4r^2)=0 b=r/2

Hence, the 3 sides are r/4, r/2 and r/4.