Indian Institute of Foreign Trade 2011 Solved Paper

Let ABC be the arc as shown in the figure. It is known that the diameter of the circle = 84 cm. Hence, the radius of the circle = 42 cm.We can see that both CO and BO are equivalent to the radius of the circle. Hence,CO=42 cm and BD=BO−OD=42−21=21cm.In triangle ODC cosDOC=

21

42

Hence ∠DOC=60°
In triangle BOC, OB = OC. Hence, we can say that ∠OCB=∠OBC=60°.
Therefore, OBC is an equilateral triangle. Hence, OB=OC=BC=42cm.
Hence, we can say that the length of the chord of ‘half of the arc’ = 42 cm. Therefore, option C is the correct answer.