 Hello and welcome to the session. In this session we discussed the following question that says three circles have the centers at A, B, C and each circle touches the other two externally. If A, B is equal to three centimeters, B, C equal to six centimeters and C, A equal to five centimeters, find the radii of the three circles. Before we move on to the solution let's recall one result according to which we have the two circles with radii R1 and R2 touch each other externally then the distance so D between the centers is equal to the sum of the radii that is R1 plus R2. This is the key idea that we use in this session. Let's proceed with the solution now. We are given three circles with centers A, B and C. So we say there are three circles with centers A, B and C and each circle touches the other two circles externally then A, B equal to three centimeters, B, C equal to six centimeters and C, A equal to five centimeters. We are supposed to find the radii of the three circles. We suppose let the radii circles with centers A, B, C with centimeters respectively. This means this circle with center A has radii as x centimeters and this circle with center D has radii as y centimeters and this circle with center C has radii z centimeters. So now we figure we have AB equal to x plus y and we know that AB is three centimeters. So therefore we get one equation x plus y equal to three. Let this be equation one. We have BC equal to y plus z which is given as six centimeters. Every equation is y plus z equal to six. Let this be equation A equal to x plus z and we know that CA is equal to five centimeters. Therefore x plus z equal to third equation. Next we add the equations one, two and three. So add in one and three we get plus y plus z is equal to three plus six plus five. This means two times x plus y plus z is equal to fourteen and from where we get x plus y plus z is equal to fourteen upon two which is equal to seven. Thus we have our first equation as x plus y plus z equal to seven. Next, track two, question four, we get, now this is our equation one. So we have x plus y plus z plus y is equal to seven minus three. This means x plus y plus z minus x minus y is equal to four. Or you can say that we get z equal to four centimeters. Then again, track two, equation two from equation four. We get as we have this is equation two that is y plus z equal to, subtract this from equation plus y plus z minus of y plus z equal to seven minus six. That is x plus y plus z minus y minus z is equal to one. This y minus y cancels z minus z cancels and we get x equal to one seventy meters. Then finally, equation three from equation four we get our equation three is x plus z equal to five and we need to subtract this from equation plus y plus z minus z is equal to seven minus plus y plus z minus x minus z equal to two. Now, z minus z cancels x minus x cancels and we have y equal to two seventy meters. And we know that x is the radius of the circle with center A, y is the radius of the circle with center B and red is the radius of the circle with center C. Therefore, with center A is equal to x seventy meters and that is equal to one centimeter. The radius of the circle center B is equal to y centimeters which is equal to two centimeters and then radius center C is equal to z centimeters and we have got the value of z of centimeters. So, this is equal to four centimeters. Here is our final answer. This completes the session. Hope you have understood the solution of this question.