Question : In an equilateral triangle, the circumradius is 14 cm. What is the length of the median in this triangle?
Option 1: $14 \sqrt{3} \mathrm{~cm}$
Option 2: $21 \mathrm{~cm}$
Option 3: $18 \sqrt{3} \mathrm{~cm}$
Option 4: $7 \sqrt{3} \mathrm{~cm}$
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Correct Answer: $21 \mathrm{~cm}$
Solution :
Circumradius = 14 cm
$a$ = side of equilateral triangle
Circum-radius, r = $\frac{a}{\sqrt{3}}$
⇒ $a = 14\sqrt{3}$ cm
Now, Length of median = Height of equilateral triangle $ = \frac{\sqrt{3}a}{2}= \frac{(\sqrt{3} × 14\sqrt{3})}{2}$ = 21 cm
Hence, the correct answer is $21 \mathrm{~cm}$.
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