Problem 91

Problem 91

Right triangles with integer coordinates

The points P (x1, y1) and Q (x2, y2) 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 ≤ x1, y1, x2, y2 ≤ 2.

Given that 0 ≤ x1, y1, x2, y2 ≤ 50, how many right triangles can be formed?


点P(x1, y1)和点Q(x2, y2)都是格点,并与原点O(0,0)构成ΔOPQ。

当点P和点Q的所有坐标都在0到2之间,也就是说0 ≤ x1, y1, x2, y2 ≤ 2时,恰好能构造出14个直角三角形。

如果0 ≤ x1, y1, x2, y2 ≤ 50,能构造出多少个直角三角形?