Difference between revisions of "Pitot Theorem"
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| + | In geometry, the '''Pitot Theorem''', named after the French engineer [[Henri Pitot]], states that in a [[tangential quadrilateral]] (one in which a circle can be inscribed) the two sums of lengths of opposite sides are the same. | ||
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| + | The theorem is a consequence of the fact that two tangent line segments from a point outside the circle to the circle have equal lengths. There are four equal pairs of tangent segments, and both sums of two sides can be decomposed into sums of these four tangent segment lengths. The converse is also true: a circle can be inscribed into every convex quadrilateral in which the lengths of opposite sides sum to the same value. | ||
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| + | == See Also == | ||
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| + | * [[Tangential quadrilateral]] | ||
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| + | === External Links === | ||
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| + | * [{{SERVER}}/community/c4h1300302 Full Proof on the AoPS forums] | ||
Latest revision as of 18:15, 22 March 2025
In geometry, the Pitot Theorem, named after the French engineer Henri Pitot, states that in a tangential quadrilateral (one in which a circle can be inscribed) the two sums of lengths of opposite sides are the same.
The theorem is a consequence of the fact that two tangent line segments from a point outside the circle to the circle have equal lengths. There are four equal pairs of tangent segments, and both sums of two sides can be decomposed into sums of these four tangent segment lengths. The converse is also true: a circle can be inscribed into every convex quadrilateral in which the lengths of opposite sides sum to the same value.
