The coordinates of points A, B and C are (6, 4), (p, 7) and (14, 18) respectively, where p is a constant. The line AB is perpendicular to the line BC.

(a) Given that p < 10, find the value of p.

A circle passes through the points A, B and C.

(b) Find the equation of the circle.

(c) Find the equation of the tangent to the circle at C, giving the answer in the form dx + ey + f = 0, where d, e and f are integers.