PlanetMath: hypotenuse

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hypotenuse

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

$\includegraphics{hyp}$

The midpoint 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 to the vertices is precisely the circumradius.

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

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

"hypotenuse" is owned by CWoo. [ full author list (2) | owner history (2) ]

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Other names:

hypothenuse

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Cross-references: Pythagorean theorem, length, circumradius, distance, diameter, circumcircle, inscribed, vertices, triangle, circumcenter, midpoint, right angle, Euclidean geometry, right triangle
There are 24 references to this entry.

This is version 11 of hypotenuse, born on 2001-12-12, modified 2007-07-07.
Object id is 1096, canonical name is Hypotenuse.
Accessed 35104 times total.

Classification:

51-00 (Geometry :: General reference works )

Pending Errata and Addenda

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