Right triangle and "G" and hypotenuse "A", then and where formula_40 is the golden ratio formula_41 Since the sides of this right triangle are in geometric progression, this is the Kepler triangle. Thales' theorem states that if "A" is any point of the circle with diameter "BC" (except "B" or "C" themselves) "ABC" is a right triangle where "A" is the right angle. The converse states that if a right triangle is inscribed in a circle then the hypotenuse will be a diameter of the circle. A corollary is that the length of the hypotenuse is twice the distance from the right
Triangle inequality that the longest side length is less than the semiperimeter. A mathematically equivalent formulation is that the area of a triangle with sides "a", "b", "c" must be a real number greater than zero. Heron's formula for the area is In terms of either area expression, the triangle inequality imposed on all sides is equivalent to the condition that the expression under the square root sign be real and greater than zero (so the area expression is real and greater than zero). The triangle inequality provides two more interesting constraints for triangles whose sides are "a, b, c", where "a