What is the area of the segment formed by a chord in a circle of radius 12 cm,
What is the area of the segment formed by a chord in a circle of radius 12 cm, if the angle subtended at the center is $150^\circ$.
12 सेमी त्रिज्या वाले एक वृत्त में एक जीवा द्वारा बनाए गए रेखाखंड का क्षेत्रफल क्या है, यदि केंद्र पर अंतरित कोण $150^\circ$ है?
Detailed Solution & Logic
Correct Answer:
$60\pi -36 $
Solution:
क्षेत्रफल (Sector)
$\frac{150}{360} \times \pi \times 12^2 = 60\pi$
त्रिभुज का क्षेत्रफल
$\frac{1}{2} \times 12^2 \times \sin 150^\circ$
$= \frac{1}{2} \times 144 \times \frac{1}{2} = 36$
वृत्तखंड (Segment) का क्षेत्रफल
$= 60\pi - 36$
सही उत्तर: ${60\pi - 36\ \text{सेमी}^2}$
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