The circle C has centre (5, 2) and passes through the point (7, 3).

(a) Find the length of the diameter of C.

(b) Find an equation for C.

(c) Show that the line y = 2x − 3 is a tangent to C and find the coordinates

of the point of contact.

Need help with question 'c'.

I know that the angle between a tangent and radius is 90 , but how would I show that the product of their gradients is -1, if I dont know the point of contact?

Also how do I find the point were it touches the circle?