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If \( \Large \left(a\ \cos \theta _{i},\ a\ \sin \theta _{i}\right)i = 1,\ 2,\ 3 \) represent the vertices of an equilateral triangle inscribed in a circle then:
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A) \( \Large \cos \theta _{1}+\cos \theta _{2}+\cos \theta _{3} = 0 \) |
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B) \( \Large \sec \theta _{1}+\sec \theta _{2}+\sec \theta _{3} = 0 \) |
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C) \( \Large \tan \theta _{1}+\tan \theta _{2}+\tan \theta _{3} = 0 \) |
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D) \( \Large \cot \theta _{1}+\cot \theta _{2}+\cot \theta _{3} = 0 \) |
Correct Answer:
| A) \( \Large \cos \theta _{1}+\cos \theta _{2}+\cos \theta _{3} = 0 \) |
Description for Correct answer:
Given points lie on a circle \( \Large x^{2}+y^{2}=a^{2} \) and in case of equilateral triangle centroid is same as circumcentre. Circumcentre of given triangle is at origin or centroid is at origin.
\( \Large \frac{ \alpha \cos \theta _{1}+ \alpha \cos \theta _{2}+ \alpha \cos\ \theta _{3}}{3} = 0 \)
and \( \Large \frac{ \alpha \sin \theta _{1}+ \alpha \sin \theta _{2}+ \alpha \sin \theta _{3}}{3} = 0 \)
\( \Large \sum \cos \theta _{1} = 0,\ \sum \sin \theta _{1} = 0 \)
Part of solved Circles questions and answers : >> Elementary Mathematics >> Circles
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