C2 tangent question on circles

Hi there, there is a question
The circle C has centre (5, 2) and passes through the point (7, 3).
(c) Show that the line y = 2x − 3 is a tangent to C and find the coordinates of the
point of contact.

How would you show this?
The equation of the circle i found is (x − 5)^2+ (y − 2)^2=5
I subbed in y = 2x − 3 into the circle to get the intersection point as (3,0)
Dont know what now.. :/
Thank you for your help!

You got one intersection point? (Hint)


Posted from TSR Mobile

Sorry I dont know what else that shows other than that there is 1 intersection.
Shoudnt I also do something to do with the radients to show they are the same?