Let ABC a right triangleMathworldPlanetmath in a Euclidean geometryMathworldPlanetmath with right angleMathworldPlanetmathPlanetmath at C. Then AB is called the hypotenuseMathworldPlanetmath of ABC.

The midpointMathworldPlanetmathPlanetmathPlanetmath P of the hypotenuse coincides with the circumcenterMathworldPlanetmath of the triangle, so it is equidistant from the three vertices. When the triangle is inscribedMathworldPlanetmath on his circumcircle, the hypotenuse becomes a diameterMathworldPlanetmathPlanetmath. So the distanceMathworldPlanetmathPlanetmath from P to the vertices is precisely the circumradius.

The hypotenuse’s length can be calculated by means of the Pythagorean theoremMathworldPlanetmathPlanetmath:

Title hypotenuse
Canonical name Hypotenuse
Date of creation 2013-03-22 12:02:58
Last modified on 2013-03-22 12:02:58
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 15
Author CWoo (3771)
Entry type Definition
Classification msc 51-00
Synonym hypothenuse
Related topic Triangle
Related topic RightTriangle
Related topic PythagorasTheorem
Related topic SohcahtoaMathworldPlanetmath