Question

In a $\triangle A B C, A B=A C=37$. Let $D$ be a point on $B C$ such that $B D=7, A D=33$. The length of $C D$ is

• A. 7
• B. 11
• C. 40
• D. not determinable

Answer 1

Answer: (C)

Given, $A B=A C=37$
$A D=33$
$B D=7$

$A B^{2}=A E^{2}+B E^{2}$ ...(i)
In $\triangle A D E$,
$A D^{2}=A E^{2}+D E^{2}$ ...(ii)
$\Rightarrow A B^{2}-A D^{2}=B E^{2}-D E^{2}$
$\Rightarrow A B^{2}-A D^{2}=(B E+D E)(B E-D E)$
$\Rightarrow A B^{2}-A D^{2}=(C E+D E)(B D) [\because BE = CE]$
$\Rightarrow A B^{2}-A D^{2}=C D \cdot B D$
$\Rightarrow C D=\frac{A B^{2}-A D^{2}}{B D}$
$\Rightarrow C D=\frac{37^{2}-33^{2}}{7}$ [given]
$\Rightarrow C D=\frac{(37+33)(37-33)}{7}$
$\Rightarrow C D=\frac{70 \times 4}{7}=40$