Question

Two poles of height $a$ and $b$ stand at the centres of two circular plots which touch each other externally at a point and the two poles subtends angles of ${30}^o$ and ${60}^o$ respectively at this point. Then the distance between the centres of these plots is:

• A. $a+b$
• B. $\frac{3a+b}{\sqrt{3}}$
• C. $\frac{a+3b}{\sqrt{3}}$
• D. $a\sqrt{3}+b$

Answer 1

The correct option is B $\frac{3a+b}{\sqrt{3}}$

In $△ABC,\tan 30°=\frac{a}{BC}$

$BC=\sqrt{3}a.......\left(1\right)$

In $△ECD,\tan 60°=\frac{b}{CD}$

$CD=\frac{b}{\sqrt{3}}.......\left(2\right)$

Required distance is equal to $BC+CD$

$BC+CD=a\sqrt{3}+\frac{b}{\sqrt{3}}=\frac{3a+b}{\sqrt{3}}$

Distance between poles$=\frac{3a+b}{\sqrt{3}}$