In a quadrilateral OABC, D is the midpoint of BC and E is the point on

1.	In a quadrilateral OABC, D is the midpoint of BC and E is the point on AD suchthat AE : ED = 2 : 1. Given that OA = a, OB = b and OC = c, express OD andOE in terms of a, b and c.
Answer» 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=2/3AD=2/3(c/2+b/2-a)=c/3+b/3-2a/3; OE=OA+AE=a+c/3+b/3-2a/3=a/3+b/3+c/3; OD=c/2+b/2; OE=a/3+b/3+c/3;

In a quadrilateral OABC, D is the midpoint of BC and E is the point on AD suchthat AE : ED = 2 : 1. Given that OA = a, OB = b and OC = c, express OD andOE in terms of a, b and c.

Answer»

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;

OD=c/2+b/2;

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

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In a quadrilateral OABC, D is the midpoint of BC and E is the point on AD suchthat AE : ED = 2 : 1. Given that OA = a, OB = b and OC = c, express OD andOE in terms of a, b and c.

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