The points A(2,7) and B(12,−3) are joined by a straight line. A point R(8,1) lies on this line and divides AB internally in the ratio m:n.
a. (i) Determine the simplest integer ratio m:n.
b. (ii) Given that m+n=15, find the individual values of m and n.
c. (iii) Using your result, calculate the length AR, leaving your answer in simplest radical form.