hypotenuse

Let $ABC$ a right triangle in a Euclidean geometry with right angle at $C$. Then $AB$ is called the hypotenuse of $ABC$.

The midpoint $P$ of the hypotenuse coincides with the circumcenter of the triangle, so it is equidistant from the three vertices. When the triangle is inscribed on his circumcircle, the hypotenuse becomes a diameter. So the distance from $P$ to the vertices is precisely the circumradius.

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

$$c=\sqrt{a^2+b^2}$$

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	Sohcahtoa