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",
Special right triangle Ancient Egypt; that their surveyors did use ropes for measurement; that Plutarch recorded in "Isis and Osiris" (around 100 AD) that the Egyptians admired the 3 : 4 : 5 triangle; and that the Berlin Papyrus 6619 from the Middle Kingdom of Egypt (before 1700 BC) stated that "the area of a square of 100 is equal to that of two smaller squares. The side of one is ½ + ¼ the side of the other." The historian of mathematics Roger L. Cooke observes that "It is hard to imagine anyone being interested in such conditions without knowing the Pythagorean