Question

In $∆\mathrm{ABC}$, $\mathrm{AD}$ is the bisector of $\angle \mathrm{A}$ meeting $\mathrm{BC}$ at $\mathrm{D}$, $\mathrm{CF}\perp \mathrm{AB}$ and $\mathrm{E}$ is the mid-point of $\mathrm{AC}$. Then median of the triangle is

• A. $\mathrm{AB}$
• B. $\mathrm{BE}$
• C. $\mathrm{FC}$
• D. $\mathrm{DE}$

Answer 1

The correct option is B

$\mathrm{BE}$

Explanation of the correct option:

Step 1 : Construction

Given: $\mathrm{E}$ is the mid point of $AC$.

Draw the figure according to the condition given in question.

Step 2: Find the median of the triangle.

Since the median of the triangle divides the triangle into two triangles of equal area.

$\mathrm{AE}=\mathrm{EC}\mathbf{}(\because \mathrm{E}\mathrm{is}\mathrm{the}\mathrm{midpoint}\mathrm{of}\mathrm{AC})$

$\therefore \mathrm{BE}$ is the median of the triangle.

Hence, option $B$ is the correct answer.