What is the area of a segment formed by a chord in a circle of radius 10 cm, when the angle subtended at center is 120°? 100𝜋

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Accepted Answer

1. Sector area: $\dfrac{120}{360}\pi r^2=\dfrac{1}{3}\pi(10)^2=\dfrac{100\pi}{3}$.  
2. Triangle area: $	frac{1}{2}r^2\sin120^\circ=	frac{1}{2}\cdot100\cdot\sin120^\circ=50\cdot	frac{\sqrt{3}}{2}=25\sqrt{3}$.  
3. Segment area = sector − triangle = $\dfrac{100\pi}{3}-25\sqrt{3}$.  
4. This equals option **(a)**.  
FINAL_ANSWER: a

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