Pitot’s Theorem

Pitot’s theorem gives us a nice fact about the side lengths of tangential quadrilaterals: the sum of one pair of opposite sides is equal to the sum of the other pair of opposite sides. We prove this result using a standard fact about tangents. There is a fallacious proof of the converse making its rounds in popular sources; though the converse is true, it is in fact hard to prove and we do not do it here.