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kevi555

Member

Registered: 2005-11-29

Posts: 1

Vector Proof Question

Hi...

For this question you have to prove it by using vector methods.

Q: Prove that medians AD and BE of triangle ABC intersect at a point that divides each median in the ratio 2:1.

Any help would be greatly appreciated.

Thanks

tz

Guest

Re: Vector Proof Question

OD = 1/2OB + 1/2OC
Let CF be the other median.

Prove that AD and BE's intersection, G divides AD in the ratio of 2:1.

Proof:

OD = 1/2OB + 1/2OC
OF = 1/2OA + 1/2OB

           OD - OF = 1/2OC - 1/2OA
     OD + 1/2OA = OF + 1/2OC
        2OD + OA = 2OD + OC
2/3OD + 1/3OA = 2/3OF + 1/3OC
                  OG = OG