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If the medians of triangle ABC intersect at P , then evaluate AB^2+AC^2+BC^2/PA^2+PB^2+PC^2

+1 vote
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If the medians of triangle ABC intersect at P , then evaluate

 AB^2+AC^2+BC^2
----------------
 PA^2+PB^2+PC^2

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posted May 1, 2016 by anonymous

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2 Answers

+1 vote

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Median Theorem ----- Va^2+Vb^2+Vc^2 = 3/4(AB^2+AC^2+BC^2)
In this triange --- Va = PA + PA/2 = 3.PA/2
Vb = PB + PB/2 = 3.PB/2
Vc = PC + PC/2 = 3.PC/2
9/4(PA^2+PB^2+PC^2) = 3/4(AB^2+AC^2+BC^2)
(AB^2+AC^2+BC^2) / (PA^2+PB^2+PC^2) = (9/4). (4/3) = 9/3 = 3

answer Aug 25, 2018 by Halil Akansel
0 votes

ans. is - (OC^2)
--------------
(OP^2)

answer May 2, 2016 by Pranali Nikam
Where is the point 'O' in the diagram?



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