Question

Suppose that the area between a pair of concentric circles is 49\pi. Find the length of a chord in the larger circle that is tangent to the smaller circle.

Answer 1

length of cord comes out to be 14

Explanation:

Given,

area of concentric circle = 49 π

area of concentric circle = π (r₁² - r₂² )

where r₁ = outer radius and

r₂ = inner radius

π (r₁² - r₂² ) = 49 π

r₁² - r₂² = 49......................(1)

from the figure you can see that

r₁² - r₂² = l²

l² = 49

l = 7

so length of cord = 2 l = 2×7 = 14

hence the length of cord comes out to be 14