The three wedges of Po

Geometry Level 3

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

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