from the legs satisfy Euler line In a right triangle, the Euler line contains the median on the hypotenuse—that is, it goes through both the right-angled vertex and the midpoint of the side opposite that vertex. This is because the right triangle's orthocenter, the intersection of its altitudes, falls on the right-angled vertex while its circumcenter, the intersection of its perpendicular bisectors of sides, falls on the midpoint of the hypotenuse. 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 In a right triangle with legs a, b and hypotenuse c, with equality only in the isosceles case. If the altitude from the hypotenuse is denoted hc, then with equality only in the isosceles case. Other properties 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. Given h > k. Let h and 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: See also Acute and obtuse triangles (oblique triangles) Spiral of Theodorus References External links Calculator for right triangles Advanced right triangle calculator Types of triangles