Relations between Various Magnitudes Which Serve as Signs of a Right-angled Triangle

We present a proven scheme of 15 relations between the sides of a triangle, the radii of incircles and excircles of the triangle, the area and half the perimeter of the triangle, which serve as signs of a right-angled triangle, together with the 16th relation which is the Pythagorean Theorem. The relations are investigated dynamically using the computerized software.