on https://en.wikipedia.org/wiki/Pythagorean_theorem#Non-Euclidean_geometry it says
However, the Pythagorean theorem remains true in hyperbolic geometry and elliptic geometry if the condition that the triangle be right is replaced with the condition that two of the angles sum to the third, say A+B = C. The sides are then related as follows: the sum of the areas of the circles with diameters a and b equals the area of the circle with diameter c.
with a link to http://link.springer.com/content/pdf/10.1007%2Fs00283-010-9169-0.pdf
in the linked pdf it speaks not of the diameter but of the radius.
Can somebody show me which of these statements (or both ) are true and how you can proof it?