Originally Posted by

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

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

$\displaystyle 2x \sqrt{4+1} = 2\sqrt{5} $

(b) Find an equation for C.

$\displaystyle (x-5)^2 + (y-2)^2 = 5 $

(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?