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# 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:

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

Related:

Triangle,RightTriangle, PythagorasTheorem, Sohcahtoa

Synonym:

hypothenuse

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

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## Corrections

hypotenuse info by drini ✓

spelling by yark ✓

isosceles triangles by Wkbj79 ✓

change one word by Mathprof ✓

reference? by Mathprof ✓

spelling by yark ✓

isosceles triangles by Wkbj79 ✓

change one word by Mathprof ✓

reference? by Mathprof ✓