Answer to Question #158501 in Geometry for Maloney

Question

1. In a quadrilateral OABC, D is the midpoint of BC and E is the point on AD such

that AE : ED = 2 : 1. Given that OA = a, OB = b and OC = c, express OD and

OE in terms of a, b and c.

Answer 1

CB=OB-OC;

CD=CB/2=(OB-OC)/2=(b-c)/2;

OD=OC+CD=c+(b-c)/2=c/2+b/2;

AD=OD-OA=c/2+b/2-a;

AE=2/3*AD=2/3*(c/2+b/2-a)=c/3+b/3-2*a/3;

OE=OA+AE=a+c/3+b/3-2*a/3=a/3+b/3+c/3;

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OD=c/2+b/2;

OE=a/3+b/3+c/3;