[tex]The\ circumference\ of\ a\ circle:C=d\pi\ (d-a\ diameter)\\-----------------------------\\\pi\approx\frac{22}{7};\ C=86\frac{26}{35}=\frac{86\cdot35+26}{35}=\frac{3036}{35}\\\\subtitute\ to\ the\ formula:\\\\\frac{3036}{35}=d\cdot\frac{22}{7}\ \ \ \ \ |divide\ both\ sides\ by\ \frac{22}{7}\ (multiply\ by\ \frac{7}{22})\\\\d=\frac{3036}{35}\cdot\frac{7}{22}\\\\d=\frac{138}{5}\cdot\frac{1}{1}\\\\\boxed{d=27.6}[/tex]