A, B, C, D, E are five coplanar points, then DA + DB + DC + AE + … - Vidyadip

MCQ

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

A
$\overline{ DE }$
✓
$3 \overline{ DE }$
C
$2 \overline{ DE }$
D
$4 \overline{ ED }$

✓

Answer

Correct option: B.

$3 \overline{ DE }$

(B) Given $A , B , C , D , E$ are five co-planar points.
Now, $\overline{ DA }+\overline{ DB }+\overline{ DC }+\overline{ AE }+\overline{ BE }+\overline{ CE }$
$\begin{array}{l}=(\overline{ DA }+\overline{ AE })+(\overline{ DB }+\overline{ BE })+(\overline{ DC }+\overline{ CE }) \\ =\overline{ DE }+\overline{ DE }+\overline{ DE }=3 \overline{ DE }\end{array}$

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