Four points A, B, C and D form a quadrilateral. Prove that it is a rectangle if and only if for an arbitrary point P we have PA^{2}+PC^{2}=PB^{2}+PD^{2}.

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## Solution

## Poem

The freight elevator

Helping us to load

In warehouses,

Shopping centers

A kind of lift with capacity

That carries charges so many

Used for goods mainly

With operators who load only

Moving with traction or hydraulic mainly

It goes up and down

Bringing you from top to the ground