Question 74

If the radius of the circumcircle of an equilateral triangle is 8 cm, then the measure of radius of its incircle is:

Solution

As per the given question,

We know that circumradius of an equilateral triangle $$(R)=\dfrac{a}{\sqrt{3}}$$

And radius of incircle $$(r) =\dfrac{a}{2\sqrt{3}}$$

Hence,

$$\dfrac{R}{r}=\dfrac{\dfrac{a}{\sqrt{3}}}{\dfrac{a}{2\sqrt{3}}}$$

$$\Rightarrow \dfrac{R}{r}=2$$

$$\Rightarrow r=\dfrac{R}{2}=\dfrac{8}{2}=4$$cm

$$\Rightarrow r=4cm$$

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