Answer to Question #158915 in Geometry for Abigail

Question

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

Given that

$OA:ED=2:1$

$OA/E=2/1$

So,

$AB=OB-OA=b-a$

So ,

$AE=AB/2=(b-a)/2$

$...Equation 1$

Similarly,

$BC=b-c$

Then,

$CD=(b-c)/2$

$...... Equation (2)$

$\therefore OD-OC=CD=(b-c)/2$

$\therefore OD-OC=(b-c)/2$

$OD-C=(b-c)/2$

$OD=C+(b+c)/2=(b+c)/2$

$\therefore OD=(b+c)/2$

Again,

$OE-OA=AE$

$OE-OA=(b-a)/2$

$OE-a=(b-a)/2$

(Given OA=a)

$OE=(a+b)/2$

$OE=(a+b)/2$