Medians AX and BY of triangle ABC are perpendicular at point G. Prove that AB = CG.

Let ∆ABC have medians AX, BY, and CZ. Let G be the centroid. Let AX ⊥ BY. Point G lies on the circle having center Z and diameter AB, because ∠AGB is a right angle. ZA = ZB = ZG AB = 2ZG Centriod

 

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