Question 67

If an equilateral triangle has side 12 cm, then what is the difference (in cm) between the circumradius and inradius?

Solution

Side of equilateral triangle = $$a=12$$ cm

=> Circumradius of equilateral triangle = $$R=\frac{a}{\sqrt3}$$ cm and inradius = $$r=\frac{a}{2\sqrt3}$$ cm

$$\therefore$$ Difference (in cm) between the circumradius and inradius

= $$\frac{a}{\sqrt3}-\frac{a}{2\sqrt3}=\frac{a}{2\sqrt3}$$

= $$\frac{12}{2\sqrt3}=\frac{6}{\sqrt3}$$

= $$2\sqrt3$$ cm

=> Ans - (C)

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