| If G is the centroid and AD is the median of \[\Delta ABC\]and\[AG=4\,\,cm,\]then DG is equal to[SSC (CGL) 2014] |
A) \[2\,\,cm\]
B) \[3\,\,cm\]
C) \[4\,\,cm\]
D) \[5\,\,cm\]
Correct Answer: A
Solution :
| G is the centroid, i.e. G is the point of intersection of medians as shown in the figure below |
 |
| In \[\Delta ABC,\] AD is the median and G is centroid. |
| We know that, medians intersect each other such that each median split in the ratio of 1: 2 from the base side. |
| \[\therefore \] \[\frac{GD}{AG}=\frac{1}{2}\] |
| \[\Rightarrow \] \[GD=\frac{1}{2}\times AG\] |
| \[=\frac{1}{2}\times 4=2\,\,cm\]\[[\because AG=4\,\,cm]\] |
| \[\therefore \]Value of DG = 2 cm |
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