You reverse what you did, so first you go 5 units down which makes the coordinates (9,1) then you move 3 units left which then is (6,1). Then you go 4 units up which lets you end out at (6,5).
As angle B is a right triangle, the sides AB and CB are perpendicular to each other. From the property of all tangents to a circle given in the beginning it can be concluded that AB is a tangent of the circle