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Question

ΔABC is an isosceles Δ with AB=AC. If BD and CE are two medians of a triangle. Prove that BD=CE.
514538_ea8c6722cba049e7b45167fc2f5b9bf6.png

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Solution

Let the sides of a ABC be a,b,b because the triangle is isosceles
Median BD=Mb=122a2+2b2b2=122a2+b2 .......(1)
Median CE=Mc=122a2+2b2b2=122a2+b2 .....(2)
As per (1) and (2) we get
Mb=Mc=122a2+b2
Thus, BD=CE

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