 Hi and welcome to the session. Today we will learn about circles and tangents to a circle. We have drawn three figures. In first case the line AB do not intersect the circle at all. So that means AB is a non-intersecting line with respect to the circle. In second case line AB intersects with the circle at two points P and Q. So here line AB is a secant of the circle and in third case line AB intersects with the circle on the point P that is at one point. So here AB is a tangent to the circle. So by this we conclude that a tangent is a line that intersects the circle at only one point. Now here at point P we cannot draw any other tangent to the circle. So that means there is only one tangent at a point of the circle. Also the common point of the tangent and the circle is called the point. So here point of contact and the tangent is said to touch the circle at the point of contact. Now let's see one important result related to tangent to the circle. This result states that the tangent at any point of a circle is perpendicular to the radius through the point of contact. Let us understand this result with the help of a figure. Here AB is a tangent to the circle with center O. Now the result says the tangent at any point let's say this point is P of a circle is perpendicular to the radius through the point of contact. Now here P is the point of contact. So this tangent will be perpendicular to the radius through the point of contact that is OP. So that means AB is perpendicular to OP. Now suppose we have a point Q on the tangent AB and we join OQ find out the length of any side if we are given the length of two sides OPQ is a right angle triangle. So let us suppose we are given OP equal to 3 centimeters, PQ equal to 4 centimeters and we need to find OQ. So here OP is 3 centimeters, PQ is 4 centimeters. Then OQ will be equal to square root of 3 square plus 4 square using Pythagoras theorem. This will be equal to 5 centimeters. So we can use this result to solve a lot of any questions. With this we finish this session. Hope you must have understood all the concepts related to circles and tangent to a circle. Goodbye, take care and have a nice day.