Pythagorean theorem Pythagorean theorem In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides "a", "b" and "c", often called the "Pythagorean equation": where "c" represents the length of the hypotenuse and "a" and "b" the lengths of the triangle's other two sides. Although it is
Incircle and excircles of a triangle has area formula_39. Similarly, formula_40 has area formula_41 and formula_42 has area formula_43. Since these three triangles decompose formula_35, we see that the area formula_45 is: where formula_48 is the area of formula_35 and formula_50 is its semiperimeter. For an alternative formula, consider formula_51. This is a right-angled triangle with one side equal to "r" and the other side equal to formula_52. The same is true for formula_53. The large triangle is composed of 6 such triangles and the total area is: The Gergonne triangle (of "ABC") is defined by the 3 touchpoints of the incircle on the 3 sides.