Question

Find the area of the major segment (in terms of π) of a circle of radius 5 cm, formed by a chord subtending an angle of 90° at the centre.

Answer 1

Area of circle = πr²

= π(5)²

= 25π

Area of minor segment = Area of sector − Area of triangle

= `90^circ/360^circ πr^2 - 1/2 xx r^2`

= `1/4 π(25) - 1/2 xx 25`

= `(25/4π - 25/2) "cm"^2`

Area of major segment = Area of circle – Area of minor segment

= `25π - (25/4π - 25/2)`

= `25π - 25/4π + 25/2`

= `(100/4π - 25/4π + 50/4)`  ....[Converting each term to a common denominator (4)]

= `(100π - 25π + 50)/4`

= `(75π + 50)/4`

= `(75π)/4 + 50/4`

= `(75/4π + 25/2) "cm"^2`