 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. Question says the radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles. First of all let us understand that if we are given a circle with radius r then area of the circle that is a is equal to pi r square. Here r represents the radius and a represents the area of the circle. Value of pi is equal to 20 upon 7. This is the key idea to solve the given question. Now let us start with the solution. We know area of the circle is equal to pi r square where r is the radius of the circle. First of all let us find out area of the circle whose radius is 8 cm. Let it be a1. Now a1 is equal to pi 8 square. We will use this formula to find the area of the circle. We know radius of the circle is 8 cm here. So substituting 8 for r in this formula we get pi 8 square cm square. Now this implies a1 is equal to pi multiplied by 64 or we can say 64 pi. Now let us find out area of a circle whose radius is 6 cm. Let it be a2. Now a2 is equal to pi multiplied by 6 square cm square. Now this implies a2 is equal to 36 pi cm square. We know area of a circle is equal to pi r square. So substituting 6 cm for r we get pi multiplied by 36. Now let us assume that the radius of the circle having area equal to sum of the areas of the given two circles be r cm and let us represent the area of this circle by a. So we can write let radius of the circle having area equal to the sum of the areas of the two given circles be r and let area of this new circle be a. The formula for area of the circle we get a is equal to pi r square. We know area of the circle is equal to pi multiplied by square of radius. So area of the new circle is equal to pi multiplied by r square. Now we know that area of the new circle is equal to the sum of the areas of the two given circles. So we can write according to the question a is equal to a1 plus a2. We have already shown above that a1 is equal to 64 pi and a2 is equal to 36 pi and a is equal to pi multiplied by r square. So substituting corresponding values of a, a1 and a2 in this expression we get pi multiplied by r square is equal to 64 pi plus 36 pi. Now dividing both the sides of this expression by pi we get r square is equal to 64 plus 36. Now we know 64 plus 36 is equal to 100 so we get r square is equal to 100. Now taking square root on both the sides we get r is equal to 10 centimeters. We know square root of 100 is equal to plus minus 10. We will neglect negative value of r we know radius cannot be negative. So neglecting negative value of r we get r is equal to 10 centimeters. So radius of this new circle is equal to 10 centimeters. So this is our required answer. This completes the session. Hope you understood the solution. Take care and keep smiling.