Question

ABC is an equilateral triangle of side 4 cm. If R ,r,h be the circumradius, inradius and altitude respectively then$\frac{R+r}{h}$

• A. 4
• B. 2
• C. 1
• D. 3

Answer 1

The correct option is C 1

Given that, $\Delta ABC$ is an equilateral triangle.

$\Rightarrow a=b=c=4$ and $A=B=C=\frac{\pi }{3}$

Now, $s=6$ and $△=\frac{\sqrt{3}{a}^2}{4}=4\sqrt{3}$

From sine rule: $\frac{a}{\sin A}=2R$
$\Rightarrow R=\frac{4}{2\sin \frac{\pi }{3}}=\frac{4}{\sqrt{3}}$

Now, $r=\frac{△}{s}=\frac{2}{\sqrt{3}}$ and $h=\frac{2△}{a}=\frac{2\times 4\sqrt{3}}{4}=\frac{6}{\sqrt{3}}$

Therefore, $\frac{R+r}{h}=1$
Ans: C