question_answer

Find the ratio of area of circumcircle and in circle of an equilateral triangle.

A)  \[2:1\]                          

B)  \[4:1\]

C)  \[\sqrt{2}:1\]                            

D)  \[1:4\]

Correct Answer: B

Solution :

Circum radius of equilateral triangle \[=\frac{Side}{\sqrt{3}}=\frac{a}{\sqrt{3}}\] In-radius of of equilateral triangle \[=\frac{side}{2\sqrt{3}}=\frac{a}{2\sqrt{3}}\] Ratio of Areas of Circumcircle and Incircle \[=\,\,\pi {{\left( \frac{a}{\sqrt{3}} \right)}^{2}}:\pi {{\left( \frac{a}{2\sqrt{3}} \right)}^{2}}\] \[=\frac{\pi {{a}^{2}}}{3}:\frac{\pi {{a}^{2}}}{4\times 3}=\underline{\mathbf{4:1}}\]