⁦The circle⁩: ⁦equation, line and circle, tangent⁩

⁦A circle is the set of points at a fixed distance r (the radius) from a fixed point (the centre)⁩. ⁦With centre C(h,k) the equation is (x − h)^٢ + (y − k)^٢ = r^٢⁩. ⁦The signs of h and k come out the opposite way in the equation⁩: ⁦the centre (٣، −٢) gives (x − ٣)^٢ + (y + ٢)^٢⁩.

⁦The general form x^٢ + y^٢ + ٢gx + ٢fy + c = ٠ has centre (−g, − f) and radius r = √(g^٢ + f^٢ − c)⁩. ⁦To find where a line meets a circle, substitute y from the line into the circle and solve the quadratic⁩: ⁦two solutions, two points; one solution, a tangent; none, the line misses the circle⁩.

⁦A tangent is perpendicular to the radius at the point of contact⁩. ⁦The length of the tangent from an outside point P to the point of contact is √(OP^٢ − r^٢), because the triangle OPT has a right angle at T⁩.