SSC
Sample Paper
SSC CHSL (10+2) Sample Test Paper-21
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 \[=\,\,\pi {{\left( \frac{a}{\sqrt{3}} \right)}^{2}}:\pi {{\left( \frac{a}{2\sqrt{3}} \right)}^{2}}\] \[=\frac{\pi {{a}^{2}}}{3}:\frac{\pi {{a}^{2}}}{4\times 3}=\underline{\mathbf{4:1}}\]