Question 69

What is the ratio of the inradius and circumradius of a square?

Solution

Let the side of square be s.

Inradius = $$\frac{s}{2}$$

In $$\triangle OAB$$,

=> OB = $$\sqrt{OA^2 + AB^2}$$

=> OB = $$\sqrt{\frac{a}{2}^2 + \frac{a}{2}^2} = \frac{a}{\sqrt{2}}$$

Their ratio would be :

$$\frac{OA}{OB} = \frac{\frac{a}{2}}{\frac{a}{\sqrt{2}}}$$

So ,the answer would be option a)$$1 : \surd{2}$$.

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