The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is ______.

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The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm. Explanation: Let r1 = 24 cm and r2 = 7 cm $\therefore$ Area of first circle = $\pi$"r"_1^2 = $\pi$(24)2 = 576$\pi$ cm2 And area of second circle = $\pi$"r"_2^2 = $\pi$(7)2 = 49$\pi$ cm2 According to the given condition, Area of circle = Area of first circle + Area of second circle $\therefore$ $\pi$R2 = 576$\pi$ + 49$\pi$ ...[Where, R be radius of circle] $\Rightarrow$ R2 = 625 $\Rightarrow$ R = 25 cm $\therefore$ Diameter of a circle = 2R = 2 $\times$ 25 = 50 cm

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