Trigonometric Equations Question 193
Question: The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is
[AIEEE 2003]
Options:
A) $ a\cot ( \frac{\pi }{n} ) $
B) $ \frac{a}{2}\cot ( \frac{\pi }{2n} ) $
C) $ a\cot ( \frac{\pi }{2n} ) $
D) $ \frac{a}{2}\cot ( \frac{\pi }{2n} ) $
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Answer:
Correct Answer: B
Solution:
- $ \tan ( \frac{\pi }{n} )=\frac{a}{2r} $ and $ \sin ( \frac{\pi }{n} )=\frac{a}{2R} $
Þ $ r+R=\frac{a}{2}[ \cot \frac{\pi }{n}+cosec\frac{\pi }{n} ] $ $ =\frac{a}{2}\cot ( \frac{\pi }{2n} ) $ .
BETA
