Question

two circle touch internally the sum of their areas is 116 Pi CM square and the distance between their Centre is 6 cm find the radius of the circle ​

Answer 1

Answer:

昨天在我辦公室附近

Step-by-step explanation:

他不知道如何在最好的課程中獲得最好的課程的唯一方法他是我們英語印地語（Hinglish）招生辦公室的主任，您對此有任何其他信息

Answer 2

Answer:

4 cm and 10 cm

Step-by-step explanation:

let radius of smaller circle be x

radius of larger circle will be x + 6

area of smaller circle = π × x^2

area of larger circle = π × (x + 6)^2

sum of areas of the two circle = 116π

$\pi {x}^{2} + \pi {(x + 6)}^{2} = 116\pi \\ \pi ({x}^{2} + {x}^{2} + 12x + 36) = 116\pi \\ 2 {x}^{2} + 12x + 36 = 116 \\ {x}^{2} + 6x + 18 = 58 \\ {x}^{2} + 6x + 18 - 58 = 0 \\ {x}^{2} + 6x - 40 = 0 \\ {x}^{2} + 10x - 4x - 40 = 0 \\ x(x + 10) - 4(x + 10) = 0 \\ (x + 10)(x - 4) = 0 \\ x + 10 = 0 \: \: \: \: x - 4 = 0 \\ x = - 10 \: \: \: \: \: \: \: \: x = 4$

we take the positive value of x= 4

the radius of smaller circle = 4 cm

radius of larger circle = x + 6 = 4 + 6 = 10 cm

verification

$\pi {4}^{2} + \pi {10}^{2} \\ = \pi( {4}^{2} + {10}^{2} ) \\ = \pi(16 + 100) \\ = 116\pi$

hope you get your answer