. Circles and Tangents In our day-to-day real life situations, we have seen two lines intersect at a point or do not intersect in a plane. For example, two parallel lines in a railway track, do not intersect. Whereas, grills in a window intersect.
Similarly what happens when a curve and a line is given in a plane? The curve may be parabola, circle or any general curve. Similarly, what happens when we consider intersection of a line and a circle? We may get three situations as given in the following diagram Figure Figure Figure O P Q O P Q O P Q (i) Straight line PQ does not touch the circle.
(i) Straight line PQ touches the circle at a common point A. (i) Straight line PQ intersects the circle at two points A and B. (ii) There is no common point between the straight line and circle. (ii) PQ is called the tangent to the circle at A.
(ii) The line PQ is called a secant of the circle. (iii) Thus the number of points of intersection of a line and circle is zero . (iii) Thus the number of points of intersection of a line and circle is one . (iii) Thus the number of points of intersection of a line and circle is two .