The points A(4,a)A(4, a)A(4,a) and B(13,6)B(13, 6)B(13,6) lie on a circle. AB AB\,AB is a diameter of the circle and has a gradient of 13\displaystyle \frac{1}{3}31. The circle has equation (x−c)2+(y−d)2=e(x - c)^2 + (y - d)^2 = e(x−c)2+(y−d)2=e where ccc, d d\,d and e e\,e are rational numbers.
Find the values of aaa, ccc, d d\,d and eee.
