 Hello friends, welcome again to another session on gems of geometry. In this session, we are going to take up another very interesting concept and this concept is called power of a point P with respect to a circle. I don't know if you've heard this or heard about this term in your regular classes, but this is very interesting and lots of theorems and properties around circles and tangents and non concentric circles and things like that will be revolving around this particular property which is called power of a point P with respect to circle. So P is any point on the plane of the circle and how is the power P defined? It is defined as D square minus R square. What is D? D is nothing but the distance between the center of the circle and the point P and R is the radius of the circle. So hence if you see here is the point P, center O, D is the distance, R is the radius. And we have calculated the value. So hence in this case if you see D is 2.24 units, R is 3. Clearly D is lesser than R because D or P is actually inside the circle. So hence power of P with respect to the circle is defined as D square minus R square. So it's coming out to be negative. Very clearly it is negative because P is inside the circle. So let us do one thing. Let us try and move this point P. So as I'm moving the point P you can see the values of the power of the point with respect to the circle is changing and till it is inside the circle it is negative. The moment it sits on B. So it's now on the circumference. So on circumference the value of the power is clearly 0. Clearly it is 0 and now the moment it comes out you can say it becomes positive. So it is positive. So all these are integral values here in this case because our R was such. R was an integer. So here there are few integral values of B. The power is better. So point being that you can define the power of the point P with respect to the circle like that. This is this concept. Lots of other theorems would be discussed. So hence knowing this definition of the power of the point with respect to the circle was important. Hope this is clear to all of you. So please remember what is power of the circle with the power of a point with respect to the circle. Nothing but difference between the square of the distance between the point and the center and the square of the radius of the circle. So that is what is called power of a point with respect to a circle. Interestingly if you see D square minus R square this thing will have some relation between the segments drawn. Or line segments from the point such that it is cutting the circle like that. So if you see this is A. Now let's say this point is B. So there will be some relation between this power of the point and the product of PC and PA. We have seen this in the previous sessions. Also D square minus R square is negative of 2 capital R and small r. So this quantity in the previous session if you see. We prove that D square minus R square wise was negative of twice capital R that is the radius and small r which is the in radius for a given triangle. You know we had seen that in the previous session. So you can check that session as well to understand what and how the power of a point with respect to a circle are related to various attributes of the circle. So we will use this concept in subsequent sessions.