The three wedges of Po

Geometry Level 3

In the figure above, there are three perpendicular wedges as shown where A=D=F=90°.\angle A=\angle D=\angle F= 90°. Further AC=DC=FC=PAC=DC=FC=P and AB=x,DE=y,FG=z.AB=x, DE=y, FG=z. The points A, C & G are collinear. Find the value of P2(1xy+1yz+1zx).P^2 \left(\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx} \right).

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