How do you know if a line is tangent to a circle?

The easiest way is to solve the system between the equation of the circle and the equation of the line. The equation that solves that system is quadratic. If the Δ of that equation is zero, the line is tangent, if it is positive the line is secant, if it is negative the line is external.Click to see full answer. Herein, how do you determine if a line is tangent or secant to a circle?A line that intersects a circle in exactly one point is called a tangent and the point where the intersection occurs is called the point of tangency. The tangent is always perpendicular to the radius drawn to the point of tangency. A secant is a line that intersects a circle in exactly two points.Similarly, how do you find the length of a line tangent to a circle? Length of the Tangent to a Circle. It is observed that |TC| is the radius of the circle, so |TC|2=g2+f2–c. This gives the length of the tangent from the point P(x1,y1) to the circle x2+y2+2gx+2fy+c=0. Herein, how do you find the tangent line of a circle? How to determine the equation of a tangent: Determine the equation of the circle and write it in the form (x−a)2+(y−b)2=r2. From the equation, determine the coordinates of the centre of the circle (a;b). Determine the gradient of the radius: mCD=y2−y1x2−x1. How do you find the point of contact of a tangent to a circle?Find point of contact when tangent and circle equations are given. If L=lx+my+n=0 is tangent to circle x2+y2+2gx+2fy+c=0 then find point of contact. I know that equation of tangent is S1=xx1+yy1+g(x+x1)+f(y+y1)+c=0 anf rearranging I obtain S1=(g+x1)x+(f+y1)y+gx1+fy1+c=0.