Question

The diagonals of the plane quadrilateral ABDC intersect at O and X,Y are the midpoints of the diagonals AB and BD respectively.show that BA+BC=2BX
and BA+BC+DA+DC=4YX

Answer 1

Answer on Question #81354 - Math - Geometry

CA=BA-BC, CX=1/2CA=1/2(BA-BC), BX=BC+CX=BC+1/2(BA-BC)=1/2(BA+BC).

YX=YB+BC+CX=YB+BA+AX=YD+DA+AX=YD+DC+CX,

YX=1/4(YB+BC+CX+YB+BA+AX+YD+DA+AX+YD+DC+CX)

=1/2(YB+YD+CX+AX)+1/4(BC+BA+DA+DC).

It is obvious that YB+YD=0, CX+AX=0. Thus YX=1/4(BC+BA+DA+DC).

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