if AD,BE and CF are the medians of triangleABC,then the value of BC.AD+CA.BE+AB.CF=
Answer (1)
21st Nov, 2020
Hey there,
In order to solve this question, you should consider the figure of the question first and then begin with the proof :
We need to prove :AD + BE +CF = 0
We may find the vectors of all 3 medians in terms of the sides of the triangle.
Vector AD ( from A to BC)= (AC/2) +( AB/2) ……….(1)
Vector BE (from B to AC)= (BA/2) + (BC/2) ………(2)
Vector CF ( from C to BA) = ( CB/2) + ( CA/2) ……….(3)
Now adding all the three equations 1,2 and 3, we get :
(AC + AB + BA + BC + CB + CA)/2
Since, CB= -BC, CA= - AC, BA= -AB
So, (AC + AB -AB+BC - BC - AC)/2
=0
Hence proved.
Thanks
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