Question : An equilateral triangle has sides of 18 cm each. The ratio of the inradius to circumradius of the triangle is:
Option 1: 2 : 1
Option 2: 3 : 2
Option 3: 3 : 4
Option 4: 1 : 2
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Correct Answer: 1 : 2
Solution :
Inradius of equilateral triangle = $\frac{\text{Side}}{2\sqrt{3}}$
Circumradius of equilateral triangle = $\frac{\text{Side}}{\sqrt{3}}$
Required ratio = $\frac{\frac{\text{Side}}{2\sqrt{3}}}{\frac{\text{Side}}{\sqrt{3}}}$
⇒ Required ratio = 1 : 2
Hence, the correct answer is 1 : 2.
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