Question

In above fig. 2, if D is mid-point of BC, the value of $\frac{cot{y}^{\circ }}{cot{x}^{\circ }}$ is:

• A. 2
• B. $\frac{1}{4}$
• C. $\frac{1}{3}$
• D. $\frac{1}{2}$

Answer 1

Answer: (D)

$\frac{1}{2}$

In $△ACD$

$\cot x^{\circ }=\frac{AC}{CD}.........\left(i\right)$

In $△ACB$

$\cot Y^{\circ }=\frac{AC}{CB}.........\left(ii\right)$

Now $D$ is the midpoint of $BC$

$\Rightarrow BC=2CD$

Dividing $\left(ii\right)$ by$\left(i\right)$

$\Rightarrow \frac{\cot y^{\circ }}{\cot x^{\circ }}=\frac{\frac{AC}{CD}}{\frac{AC}{CB}}=\frac{CB}{CD}=\frac{CB}{2CB}=\frac{1}{2}$

So option $D$ is correct.