Pitot theorem

The Pitot theorem in geometry states that in a tangential quadrilateral the two pairs of opposite sides have the same total length.

Pitot's theorem states that, for these quadrilaterals, the two sums of lengths of opposite sides are the same.

Both sums of lengths equal the semiperimeter of the quadrilateral.

[2] The converse implication is also true: whenever a convex quadrilateral has pairs of opposite sides with the same sums of lengths, it has an inscribed circle.

This divides the four sides into eight segments, between a vertex of the quadrilateral and a point of tangency with the circle.