In ncert class 10 the chapter Areas Related To Circles what is the best solution of exercise 12.1 question number 2 , please help me to solve this question in a easiest and simple way .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.

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# 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. Q.2

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Radius of 1

^{st}Â circle = 8 cm (given)âˆ´ Area of 1

^{st}Â circle = Ï€(8)^{2}Â = 64Ï€Radius of 2

^{nd}Â circle = 6 cm (given)âˆ´ Area of 2

^{nd}Â circle = Ï€(6)^{2}Â = 36Ï€So,

The sum of 1

^{st}Â and 2^{nd}Â circle will be = 64Ï€+36Ï€ = 100Ï€Now, assume that the radius of 3

^{rd}Â circle = Râˆ´ Area of the circle 3

^{rd}Â circle = Ï€R^{2}It is given that the area of the circle 3

^{rd}Â circle = Area of 1^{st}Â circle + Area of 2^{nd}Â circleOr, Ï€R

^{2}Â = 100Ï€cm^{2}R

^{2}Â = 100cm^{2}So, R = 10cm