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JEE Class main Answered

Sir pls solve the following.

Asked by rsudipto | 05 Jan, 2019, 09:19: AM
Expert Answer
By thereom we can say that in triangle ABC where G is the centroid of the triangle.
AB2 + BC2 + CA2 = 3(GA2 + GB2 + GC2)
Hence, GA2 + GB2 + GC2 = 1/3 (a2 + b2 + c2)
This can be proved using distance formula.

Consider, A(x1, y1), B(x2, y2) and C(x3, y3) hence, begin mathsize 16px style straight G equals open parentheses fraction numerator straight x subscript 1 plus straight x subscript 2 plus straight x subscript 3 over denominator 3 end fraction comma fraction numerator straight y subscript 1 plus straight y subscript 2 plus straight y subscript 3 over denominator 3 end fraction close parentheses end style
Assuming that G(0, 0) we will find AB2 + BC2 + CA2 and 3(GA2 + GB2 + GC2) we will get AB2 + BC2 + CA2 = 3(GA2 + GB2 + GC2)
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