Find the area of the region between the two concentric circles, if the length of a chord of the outer circle just touching the inner circle at a particular point on it is 10 cm (Take, `pi = (22)/(7)`)

Explanation

Let the chord AB touch the inner circle at C and let O be the centre of both the circles, then
`OC = r, OA = R and AB = 10 cm`
Now, since `OC bot AB` ( `:'` radius through point of contact is perpendicular to the tangent)
`:.` C is the mid-point of AB
(`:' bot` drawn from the centre of the chord, bisects the chord)
`rArr AC = (1)/(2) AB = (1)/(2) xx 10 = 5 cm`
Now, in right `Delta OCA`
`OA^(2) = OC^(2) + AC^(2)` (by Pythagoras theorem)
`rArr R^(2) - r^(2) = 25` ...(1)
`:.` The required area of region between two concentric circle
`= pi R^(2) - pi r^(2) = pi (R^(2) - r^(2)) = 25 pi` [from (1)]
`= 25 xx (22)/(7) = 78.57 cm^(2)`