## Right triangles with integer coordinates

### Problem 91

Published on Friday, 18th March 2005, 06:00 pm; Solved by 10021; Difficulty rating: 25%The points P (*x*_{1}, *y*_{1}) and Q (*x*_{2}, *y*_{2}) are plotted at integer co-ordinates and are joined to the origin, O(0,0), to form ΔOPQ.

There are exactly fourteen triangles containing a right angle that can be formed when each co-ordinate lies between 0 and 2 inclusive; that is,

0 ≤ *x*_{1}, *y*_{1}, *x*_{2}, *y*_{2} ≤ 2.

Given that 0 ≤ *x*_{1}, *y*_{1}, *x*_{2}, *y*_{2} ≤ 50, how many right triangles can be formed?