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prove that 3 times the squares of the sides of a triangle is equal to four times the sum of the square of the medians

prove that 3 times the squares of the sides of a triangle is equal to four times the sum of the square of the medians

Grade:12

2 Answers

Sunil Raikwar
askIITians Faculty 45 Points
6 years ago
Hello students
please find the solution of your question below:

by Appollonious theorem we know that
AB^2 + AC^2 = 2(AD^2+BD^2)............1 { WHERE AD IS MEDIAN OF TRIANGLE ABC)
SIMILARLY
BC^2 + AB^2 = 2(BE^2+ CE^2).............2
CA^2 + BC^2 = 2(CF^2 + BF^2)..........3
ADDIND 1,2,3, WE GET
3(AB^2 + BC^2 + CA^2) = 4(AD^2 +BE^2 + CF^2) { BD=BC/C & SO ON)
S. Haris Ahmed Irfan
29 Points
6 years ago
what is appollnious thereom?

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