The Pitot Theorem states that a convex quadrilateral has an inscribed circle tangent to all four sides if and only if the sums of the lengths of its two pairs of opposite sides are equal. Named for Henri Pitot, it is a classical characterization of tangential quadrilaterals, the quadrilateral counterpart to the simpler fact that every triangle always has an inscribed circle.
Facts
StatementIn a tangential quadrilateral the two pairs of opposite sides have the same total length. 1 Classification
Statement Form Connections
Has Statement Form
In Branch
Source Pitot theorem (Wikipedia)
Proved By
Source Pitot theorem (Wikipedia)
Sources
1. Pitot theorem (Wikipedia)
Statement and converse, first sentence
in a tangential quadrilateral the two pairs of opposite sides have the same total length.
- History: Henri Pitot proved his theorem in 1725
In Branch: Geometry, Lead sentence
The Pitot theorem in geometry states that in a tangential quadrilateral the two pairs of opposite sides have the same total length
Proved By: Jakob Steiner, Lead
Henri Pitot proved his theorem in 1725, whereas the converse was proved by the Swiss mathematician Jakob Steiner in 1846.
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