Prove that $a^2(p-q)(p-r)+ b^2(q-r)(q-p)+ c^2(r-p)(r-q) =4(\delta)^2$ If $p$,$q$,$r$ are the perpendiculars drawn from the vertices of a triangle ABC upon any straight line meeting the sides externally in D,E,F. 

where a,b,c are the sides opposite to angles A,B,C in Triangle ABC and delta represents the area of the triangle ABC.
Also prove that EF= $(2pq)/((p-q)(p-r))$
I have tried this problem in this way but couldn't solve the problem, can anyone help me from here??
Let G,H,I be the foot of perpendiculars from A,B and C. GH=x GI=y check the following pictures carefully.we have broke the figure into rectangles and applied Pythagoras theorem...breaking the figure and applying Pythagoras theorem is very important

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Let G,H,I be the foot of perpendiculars from A,B and C. GH=x GI=y check the following pictures carefully.we have broke the figure into rectangles and applied Pythagoras theorem...breaking the figure and applying Pythagoras theorem is very important

]1