Editing Right triangle (section)

==Inequalities==

In any right triangle the diameter of the incircle is less than half the hypotenuse, and more strongly it is less than or equal to the hypotenuse times <math>(\sqrt{2}-1).</math><ref name=PL>Posamentier, Alfred S., and Lehmann, Ingmar. ''[[The Secrets of Triangles]]''. Prometheus Books, 2012.</ref>{{rp|p.281}}

In a right triangle with legs <math>a,b</math> and hypotenuse <math>c,</math>

:<math>c \geq \frac{\sqrt{2}}{2}(a+b)</math>

with equality only in the isosceles case.<ref name=PL/>{{rp|p.282, p.358}}

If the altitude from the hypotenuse is denoted <math>h_c,</math> then

:<math>h_c \leq \frac{\sqrt {2}}{4}(a+b)</math>

with equality only in the isosceles case.<ref name=PL/>{{rp|p.282}}