A chord of a circle of radius 42 cm subtends a right angle at the center. Find the area of the corresponding major segment. [π=227]
Answer:
5040 cm2
- We know that area of minor sector =θ360×πr2
Substituting the value of θ and r in the formula, we have
Area of sector OAB=90360×227×(42)2=1386 cm2 - Also, area of a right-angled triangle = 12×Base×Height
So, area of right-angled △OAB=12×OA×OB=12×42×42=882 cm2 - Now, area of minor segment = area of minor sector OAB − area of △OAB=1386−882=504 cm2
- Area of major segment = area of the circle − area of minor segment =π(42)2−504=5544−504=5040 cm2