Question

In triangle, P, Q and R are the mid points of AB, BC and AC respectively. If D is any point then express DA+DB+DC interms of DP, DQ AND DR.

Answer 1

DA + DB +DC = 2 (DP + DQ + DR )

Step-by-step explanation:

Given:

Here, in triangle, P, Q and R are the mid points of AB, BC and AC respectively.

Also, D is any point.

Now,

In ABC, AQ, BR, CP are the median.

Consider point D is at the intersections of all medians & we know by theorem by median , we have

$\frac{AD}{DQ} = \frac{2}{1} \Rightarrow AD=2DQ$          [1]

$\frac{BD}{DR} = \frac{2}{1}\Rightarrow BD=2DR$          [2]

$\frac{CD}{DP} = \frac{2}{1}\Rightarrow CD=2DP$          [3]

Adding Eq (1), (2), (3), we get

DA + DB + DC = 2DQ + 2DR + 2DP

DA + DB +DC = 2 (DP + DQ + DR )

Answer 2

so this is the answer guys