Editing Right triangle (section)

==Other properties==
If segments of lengths <math>p</math> and <math>q</math> emanating from vertex <math>C</math> trisect the hypotenuse into segments of length <math>\tfrac13 c,</math> then<ref name=Posamentier>Posamentier, Alfred S., and Salkind, Charles T. ''Challenging Problems in Geometry'', Dover, 1996.</ref>{{rp|pp. 216–217}}
:<math>p^2 + q^2 = 5\left(\frac{c}{3}\right)^2.</math>

The right triangle is the only triangle having two, rather than one or three, distinct inscribed squares.<ref>Bailey, Herbert, and DeTemple, Duane, "Squares inscribed in angles and triangles", ''[[Mathematics Magazine]]'' 71(4), 1998, 278–284.</ref>

Given any two positive numbers <math>h</math> and <math>k</math> with <math>h > k.</math> Let <math>h</math> and <math>k</math>  be the sides of the two inscribed squares in a right triangle with hypotenuse <math>c.</math> Then
:<math>\frac{1}{c^2} + \frac{1}{h^2} = \frac{1}{k^2}.</math>

These sides and the incircle radius <math>r</math> are related by a similar formula:

:<math>\frac{1}{r}=-{\frac{1}{c}}+\frac{1}{h}+\frac{1}{k}.</math>

The perimeter of a right triangle equals the sum of the radii of [[Incircle|the incircle and the three excircles]]:

:<math>a+b+c=r+r_a+r_b+r_c.</math>