Question

A chord 10 cm long is drawn in a circle whose radius is  `5sqrt(2)` cm. Find the areas of both the segments.

Answer 1

Let O be the centre of the circle and AB be the chord.

Consider Δ OAB.

OA = OB = `5sqrt(2)  "cm"`

OA2 + OB = 50 + 50 = 100

Now, 

`sqrt(100) = 10  "cm" = "AB"`

Thus, ΔOAB is a right isosceles triangle.

Thus we have :

Area of Δ OAB `=1/2xx5sqrt(2)xx5sqrt(2) = 25  "cm"^2`

Area of the minor segment = Area of the sector - Area of the triangle

`=(90/360xxpixx(5sqrt(2))^2) - 25`

= 14.25 cm² 

Area of the major segment = Area of the circle -- Area of the minor segment

`= pixx(5sqrt(2))^2-14.25`

= 142.75 cm²