Here are sets of 3 Pythagorean triangles with equal perimeters and area in arithmetic progression.

Note that the perimeters are multiples of 120.

The pattern breaks in this example:

The perimeter is not a multiple of 120.

Find other sets of 3 Pythagorean triangles with equal perimeters that are not multiples of 120.

……………….. **#2** ………………..

__multiples of 120 appear again__ :

Notice that the radius of incircle of the first triple in each set is a multiple of 120

……………….. **#3** ………………..

__No multiples of 120__ :

……………….. **#4** ………………..

One triple is primitive in each set:

Find other such sets – that include a primitive – as shown in **#4**