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 PA²+PC²=PB²+PD².

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

Bella