Problem 91

Right triangles with integer coordinates

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?

**
These problems are part of
Project Euler
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CC BY-NC-SA 2.0 UK
**