Question

a chord of a circle of radius 10cm substends a right angle at the centre. find the area of the corresponding major segment

Answer 1

Radius of the circle = 10 cm

Major segment is making 360° - 90° = 270°

Area of the sector making angle 270° 

                                 = (270°/360°) × π r2 cm2

                                           = (3/4) × 102π  = 75 π cm2 
                                = 75 × 3.14 cm2 = 235.5 cm2 
∴ Area of the major segment = 235.5 cm2

Height of ΔAOB = OA = 10 cm

Base of ΔAOB = OB = 10 cm

Area of ΔAOB = 1/2 × OA × OB

                         = 1/2 ×10 × 10 = 50 cm2

Major segment is making  90°

 Area of the sector making angle 90°        

= (90°/360°) × π r2 cm2

                                          = (1/4) × 102π  = 25 π cm2 
                               = 25 × 3.14 cm2 = 78.5 cm2 
Area of the minor segment = Area of the sector making angle 90° - Area of ΔAOB

                                            = 78.5 cm2 -  50 cm2 = 28.5 cm2