Right triangle then with equality only in the isosceles case. If segments of lengths "p" and "q" emanating from vertex "C" trisect the hypotenuse into segments of length "c"/3, then The right triangle is the only triangle having two, rather than one or three, distinct inscribed squares. Let "h" and "k" ("h" > "k") be the sides of the two inscribed squares in a right triangle with hypotenuse "c". Then These sides and the incircle radius "r" are related by a similar formula: The perimeter of a right triangle equals the sum of the radii of the incircle and the three excircles:
Altitude (triangle) the tangential triangle, and the center of similitude of the orthic and tangential triangles, are on the Euler line. Trilinear coordinates for the vertices of the tangential triangle are given by For more information on the orthic triangle, see here. For any triangle with sides and semiperimeter , the altitude from side is given by This follows from combining Heron's formula for the area of a triangle in terms of the sides with the area formula (1/2)×base×height, where the base is taken as side and the height is the altitude from . Consider an arbitrary triangle with sides and with