 Hello and welcome to the session. In this session, we will discuss a question which says that the radar of two circles are 12 centimeters and 16 centimeters respectively. Find the radius of the circle whose area is equal to the sum of the areas of two circles. And the options are A, 30 centimeters, B, 18 centimeters, C, 20 centimeters, and D, 20 X centimeters. Now before starting the solution of this question, we should know our result. And that is the area of the circle is equal to pi r square where r is the radius of the circle and pi is the constant. Now this result will work out as a key idea for solving out this question. And now we will start with the solution. Now in the question, the area of the two circles are 12 centimeters and 16 centimeters respectively. Now let the first circle radius be r1 and given r1 is equal to 12 centimeters. Therefore, according to the result which is given in the key idea, area of the first circle will be equal to pi r1 square which is equal to, now r1 here is 12 centimeters so this will be pi into 12 into 12 centimeters square which is equal to 144 pi centimeters square. Now let the second circle be r2 and given 2 is equal to 16 centimeters. Second circle equal to pi r2 square 16 centimeters so it will be pi into 16 into 16 centimeters square which is equal to 256 pi centimeters square. Now let the third circle the radius be r third circle is equal to pi. Now we have to find the radius of the circle which we have taken as a third circle whose area is equal to the term of the areas of the two circles which we have taken as circle 1 and circle 2. So according to question, we have the third circle equal to area. Now this is the area of the first circle, this is the area of the second circle and this is the area of the third circle. So this is 20 meters square plus 256 pi centimeters square which further implies 200 pi centimeters square. Further implies where pi will be cancelled with pi so r square is equal to 400 centimeters square which further implies r is equal to 20 centimeters. The required radius is equal to 20 centimeters. This is equal to 20 centimeters solution of the given question and that's all for this session. Hope you all have enjoyed this session.