Properties of Triangles 3 Question 14
14. A polygon of nine sides, each of length 2 , is inscribed in a circle. The radius of the circle is… .
$(1987,2 M)$
Analytical & Descriptive Questions
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Answer:
Correct Answer: 14. $\operatorname{cosec} 20^{\circ}$
Solution:
- Here, central angle $=\frac{360^{\circ}}{9}=40^{\circ}$
In $\triangle A C M$,
$$ \frac{1}{r}=\sin 20^{\circ} $$
$\Rightarrow \quad r=\operatorname{cosec} 20^{\circ}$
$\therefore$ Radius of circle $=\operatorname{cosec} 20^{\circ}$
