 Hi friends, so welcome to a session on geometry and we are going to start up with Circles, okay, so what is a circle guys? If you know from your basic definition since your childhood you have been taught about all of this So circle is all around you if you can see a coin a Bangal, you know the Sun appears to be circular during the daytime when the full moon is circular So there are so many, you know Circular circle Around you. So hence we are going to describe circles define circles different parts of circles properties of circles And you know what Euclid the famous mathematician of Before Christian era times. He has done a lot of work on circles and related theorems So we will be discussing all those properties of circles and Different theorems and axioms related to it. So let's begin first of all will define circle So a circle is defined as a path Traced by a point on a plane, okay with certain conditions now, please Keep this definition, you know in your mind always. So a circle is defined in a plane, right? So you must have a plane first and then it is defined as a path Raised out by a point which is equidistant from another point on the same plane, okay? So let's begin by drawing it. So I am drawing a Point a here and I drew this circle, right? So point B is on the circle and a is called the center of the circle now Let me just draw another point here See let's say now if you see if I move this point C, you know, so I'm moving this point C And as I am moving, you know, it is it is tracing a path Which the path is the circle itself. Can you see and there's interesting fact about this movement? What is it? Let me measure the distance between a and C, okay, so let me measure the distance of between a and C it is six Six units in this case. It is six centimeter. Okay, so let me just yeah, take it away and let me also join this Point a to point C. Okay. Now this AC guys AC this point AC this line AC is nothing but the Radius of this circle, this is called the radius of the circle now watch this So if I'm moving this point C now, so let me just move this point C Can you see I am moving the point C. Let me just eliminate this extra Thing yeah, so I am now moving point C and if you see Always it is having a distance of six units from the center. Isn't it? So this is the Important fact about the circle. So what did we learn about this? So there is a point C which is moving on a plane Such that its distance from another point on the same plane again reemphasizing same plane is Constant and this value in this case is six, right? I would have moved this so if you know, I am changing the Circle, you know the value of AC the radius and you can see in This case also C is moving on the same Path so this path traced out. It's called. Let me trace the path of C. So you'll get to see that You know, it is nothing but it is falling on the circle itself. Can you see guys now? I am tracing the path of See so as C is moving I am tracing the path if you see as C is moving such that it is making It is you know not changing its distance from point a which is also called the center and And You'll see it traces out a perfect circle. Isn't it see it is it is tracing out So wherever point C is going it is tracing out This particular path and this path is nothing but a circle, right? So this is what is definition of circle guys, right? Now any point within this periphery Let's say if I take a point B here, right and join AD, okay? So let me join AD and let me measure AD as well. So if you see this is five point eight five What is the value five point eight five? Isn't it which is clearly less than eight that is the radius, right? And let me take another point here E and let me join the points A and E. So I joined A and E Okay. Now, let me measure this. So how much is this distance a E? So if you see a is ten point six one, right? So hence as if I move a E. Let's say Let me move the point E. So as I am, you know, so as E moves It is always more than eight. Can you see and as I go toward the center? The distance a E is reducing and on the circle It is it and you see now E is sitting on the circle So it is equal to the radius the distance from the center is equal to the radius eight as it comes in The value AE Changes and reduces from below it, right and at the center it becomes zero. So if you see Anywhere all these points wherever E is there with the radius or so distance is less than the radius This part is called the internal part region internal region of the circle and This part where the radius is more than the rate, you know Oh, sorry the distance between E and a is more than the radius is called external part of or external region to the circle and There is a third thing which is the circle itself. So we see The circle is dividing the plane into two parts internal region and External region. So you may count the circle itself into the internal region. So, right? So there are two parts of the plane If you are discounting the circle itself the outside of circle and inside of outside the distance between the point Any point outside the circle the distance between the point and Center will be more than the radius and any point inside the circle the distance between the center and the point itself Will be less than the radius. So this is what we learned in the first session so for this, you know for more properties and attributes of circle will Will you know go through all of them in the next session. Thank you