Question

If $A,B,C,D$ and $E$ are five coplanar points, then the value of $\overline{DA}+\overline{DB}+\overline{DC}+\overline{AE}+\overline{BE}+\overline{CE}$, is equal to

• A. $\overline{DE}$
• B. $2\left(\overline{DE}\right)$
• C. $3\left(\overline{DE}\right)$
• D. $4\left(\overline{DE}\right)$

Answer 1

Answer: (C)

$3\left(\overline{DE}\right)$

Given that,

$A,B,C,D$ are coplanar points.

Now,

$\begin{array}{c}\overline{D}A+\overline{D}B+\overline{D}C+\overline{A}E+\overline{B}E+\overline{C}E\\ =\left(\overline{D}A+\overline{A}E\right)+\left(\overline{D}B+\overline{B}E\right)+\left(\overline{D}C+\overline{C}E\right)\\ =\overline{D}E+\overline{D}E+\overline{D}E\\ =3\overline{D}E\end{array}$

Hence,

Option $C$ is correct answer.