Right triangle 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. 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 formula_44 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 "h",
Kepler triangle if and only if that triangle is a Kepler triangle. A Kepler triangle can be constructed with only straightedge and compass by first creating a golden rectangle: Kepler constructed it differently. In a letter to his former professor Michael Mästlin, he wrote, "If on a line which is divided in extreme and mean ratio one constructs a right angled triangle, such that the right angle is on the perpendicular put at the section point, then the smaller leg will equal the larger segment of the divided line." In the Kepler triangle with sides formula_8 consider: Then the perimeters of the