A chord of a circle of radius 42 cm42 cm subtends a right angle at the center. Find the area of the corresponding major segment. [π=227][π=227]
O A B 90°


Answer:

5040 cm25040 cm2

Step by Step Explanation:
  1. We know that area of minor sector =θ360×πr2=θ360×πr2

    Substituting the value of θθ and rr in the formula, we have

    Area of sector OAB=90360×227×(42)2=1386 cm2OAB=90360×227×(42)2=1386 cm2
  2. Also, area of a right-angled triangle = 12×Base×Height12×Base×Height

    So, area of right-angled OAB=12×OA×OB=12×42×42=882 cm2OAB=12×OA×OB=12×42×42=882 cm2
  3. Now, area of minor segment = area of minor sector OABOAB area of OAB=1386882=504 cm2OAB=1386882=504 cm2
  4. Area of major segment == area of the circle area of minor segment =π(42)2504=5544504=5040 cm2

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