Difference between revisions of "The Pitot Theorem"
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In geometry, the Pitot theorem, named after the French engineer Henri Pitot, states that in a tangential quadrilateral (i.e. one in which a circle can be inscribed) the two sums of lengths of opposite sides are the same. | In geometry, the Pitot theorem, named after the French engineer Henri Pitot, states that in a tangential quadrilateral (i.e. one in which a circle can be inscribed) the two sums of lengths of opposite sides are the same. | ||
Latest revision as of 18:11, 2 September 2016
http://wiki-images.artofproblemsolving.com/f/fe/Pitot_theorem.svg.png In geometry, the Pitot theorem, named after the French engineer Henri Pitot, states that in a tangential quadrilateral (i.e. 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.
For a full proof go to this link:http://artofproblemsolving.com/community/c4h1300302_this_a_better_problem_than_that_fe_geometry
