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a chord of a circle of radius 10cm subtends a right angle at the centre. find the area of the corresponding:i)minor segment ii)major sector.(use phy=3.14)

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A chord of circle 10cm subtends a right angle at the centre. Find the area

A chord of circle 10cm subtends a right angle at the centre. Find the area of the corresponding : minor segmemt 2 major segment

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asked Oct 30, 2017 by tendulkar.2001



1 Answer



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