1. The problem statement, all variables and given/known data Ok so this is a question from last years past paper of my course: X= 1/2 intersects the circle that is centered at origin at two points, one of which is in the lower half plane y<0; what is the equation of the tangent tot the same circle at this point? 2. Relevant equations So basically x = 1/2 intersects the circle twice, so the points at which it intersects would have co-ordinates 1/2, y and I would use these to find radius to find the gradient of the x = tangent. But so far I have been unable to find a value for the raidus or the point y where the circle intersects x = 1/2. I have gotten ansers with respect to y but can not find the value of it and hence I am stuck 3. The attempt at a solution forumla of the circle = X^2 + y^2 = r^2 so r^2 = 1/4 + y^2 Then i try to find the gradient of radius (0,0) to (1/2, y) which is 2y so the radius of the gradient of the tangent line is -1/2y but what is y :S am i missing something very obvious here? Please help. Thank you.